Add comprehensive statistical distribution functions to DuckDB, enabling advanced statistical analysis, probability calculations, and random sampling directly within SQL queries.
Maintainer(s):
rustyconover
Compatibility Matrix
This table covers all DuckDB releases that have not reached end-of-life, including LTS releases, and shows the 2 most recent patch releases of each. Older patch releases are not listed, but the extension may be available for them as well.
| Platform | 1.4.4 | 1.4.5 | 1.5.5 | 1.5.6 | 2.0.0 |
|---|---|---|---|---|---|
| Linux AMD64 | |||||
| Linux ARM64 | |||||
| macOS AMD64 | |||||
| macOS ARM64 | |||||
| Windows AMD64 | |||||
| Windows ARM64 | |||||
| WebAssembly |
Installing and Loading
INSTALL stochastic FROM community;
LOAD stochastic;
About stochastic
For more information regarding usage, see the documentation.
Added Functions
| function_name | function_type | description | comment | examples |
|---|---|---|---|---|
| dist_bernoulli_cdf | scalar | Computes the cumulative distribution function (CDF) of the bernoulli distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_bernoulli_cdf(0.5, 0)] |
| dist_bernoulli_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the bernoulli distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_bernoulli_cdf_complement(0.5, 0)] |
| dist_bernoulli_chf | scalar | Computes the cumulative hazard function of the bernoulli distribution. | NULL | [dist_bernoulli_chf(0.5, 0)] |
| dist_bernoulli_hazard | scalar | Computes the hazard function of the bernoulli distribution. | NULL | [dist_bernoulli_hazard(0.5, 0)] |
| dist_bernoulli_kurtosis | scalar | Returns the kurtosis of the bernoulli distribution. | NULL | [dist_bernoulli_kurtosis(0.5)] |
| dist_bernoulli_kurtosis_excess | scalar | Returns the excess kurtosis of the bernoulli distribution. | NULL | [dist_bernoulli_kurtosis_excess(0.5)] |
| dist_bernoulli_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the bernoulli distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_bernoulli_log_cdf(0.5, 0)] |
| dist_bernoulli_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the bernoulli distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_bernoulli_log_cdf_complement(0.5, 0)] |
| dist_bernoulli_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the bernoulli distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_bernoulli_log_pdf(0.5, 1)] |
| dist_bernoulli_mean | scalar | Returns the mean (μ) of the bernoulli distribution, which is the first moment. | NULL | [dist_bernoulli_mean(0.5)] |
| dist_bernoulli_median | scalar | Returns the median (50th percentile) of the bernoulli distribution, which equals the mean. | NULL | [dist_bernoulli_median(0.5)] |
| dist_bernoulli_mode | scalar | Returns the mode (most likely value) of the bernoulli distribution, which equals the mean. | NULL | [dist_bernoulli_mode(0.5)] |
| dist_bernoulli_pdf | scalar | Computes the probability density function (PDF) of the bernoulli distribution. Returns the probability densityat point x for a bernoulli distribution with specified parameters. | NULL | [dist_bernoulli_pdf(0.5, 1)] |
| dist_bernoulli_quantile | scalar | Computes the quantile function (inverse CDF) of the bernoulli distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_bernoulli_quantile(0.5, 0.95)] |
| dist_bernoulli_quantile_complement | scalar | Computes the complementary quantile function of the bernoulli distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_bernoulli_quantile_complement(0.5, 0.05)] |
| dist_bernoulli_range | scalar | Returns the range of the bernoulli distribution. | NULL | [dist_bernoulli_range(0.5)] |
| dist_bernoulli_sample | scalar | Generates random samples from the bernoulli distribution with specified parameters. | NULL | [dist_bernoulli_sample(0.5)] |
| dist_bernoulli_skewness | scalar | Returns the skewness of the bernoulli distribution. | NULL | [dist_bernoulli_skewness(0.5)] |
| dist_bernoulli_stddev | scalar | Returns the standard deviation (σ) of the bernoulli distribution. | NULL | [dist_bernoulli_stddev(0.5)] |
| dist_bernoulli_support | scalar | Returns the support of the bernoulli distribution. | NULL | [dist_bernoulli_support(0.5)] |
| dist_bernoulli_variance | scalar | Returns the variance (σ²) of the bernoulli distribution. | NULL | [dist_bernoulli_variance(0.5)] |
| dist_beta_cdf | scalar | Computes the cumulative distribution function (CDF) of the beta distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_beta_cdf(2.0, 5.0, 0.5)] |
| dist_beta_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the beta distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_beta_cdf_complement(2.0, 5.0, 0.5)] |
| dist_beta_chf | scalar | Computes the cumulative hazard function of the beta distribution. | NULL | [dist_beta_chf(2.0, 5.0, 0.5)] |
| dist_beta_hazard | scalar | Computes the hazard function of the beta distribution. | NULL | [dist_beta_hazard(2.0, 5.0, 0.5)] |
| dist_beta_kurtosis | scalar | Returns the kurtosis of the beta distribution. | NULL | [dist_beta_kurtosis(2.0, 5.0)] |
| dist_beta_kurtosis_excess | scalar | Returns the excess kurtosis of the beta distribution. | NULL | [dist_beta_kurtosis_excess(2.0, 5.0)] |
| dist_beta_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the beta distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_beta_log_cdf(2.0, 5.0, 0.5)] |
| dist_beta_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the beta distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_beta_log_cdf_complement(2.0, 5.0, 0.5)] |
| dist_beta_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the beta distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_beta_log_pdf(2.0, 5.0, 0.5)] |
| dist_beta_mean | scalar | Returns the mean (μ) of the beta distribution, which is the first moment. | NULL | [dist_beta_mean(2.0, 5.0)] |
| dist_beta_median | scalar | Returns the median (50th percentile) of the beta distribution, which equals the mean. | NULL | [dist_beta_median(2.0, 5.0)] |
| dist_beta_mode | scalar | Returns the mode (most likely value) of the beta distribution, which equals the mean. | NULL | [dist_beta_mode(2.0, 5.0)] |
| dist_beta_pdf | scalar | Computes the probability density function (PDF) of the beta distribution. Returns the probability densityat point x for a beta distribution with specified parameters. | NULL | [dist_beta_pdf(2.0, 5.0, 0.5)] |
| dist_beta_quantile | scalar | Computes the quantile function (inverse CDF) of the beta distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_beta_quantile(2.0, 5.0, 0.95)] |
| dist_beta_quantile_complement | scalar | Computes the complementary quantile function of the beta distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_beta_quantile_complement(2.0, 5.0, 0.05)] |
| dist_beta_range | scalar | Returns the range of the beta distribution. | NULL | [dist_beta_range(2.0, 5.0)] |
| dist_beta_sample | scalar | Generates random samples from the beta distribution with specified parameters. | NULL | [dist_beta_sample(2.0, 5.0)] |
| dist_beta_skewness | scalar | Returns the skewness of the beta distribution. | NULL | [dist_beta_skewness(2.0, 5.0)] |
| dist_beta_stddev | scalar | Returns the standard deviation (σ) of the beta distribution. | NULL | [dist_beta_stddev(2.0, 5.0)] |
| dist_beta_support | scalar | Returns the support of the beta distribution. | NULL | [dist_beta_support(2.0, 5.0)] |
| dist_beta_variance | scalar | Returns the variance (σ²) of the beta distribution. | NULL | [dist_beta_variance(2.0, 5.0)] |
| dist_binomial_cdf | scalar | Computes the cumulative distribution function (CDF) of the binomial distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_binomial_cdf(10, 0.5, 5)] |
| dist_binomial_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the binomial distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_binomial_cdf_complement(10, 0.5, 5)] |
| dist_binomial_chf | scalar | Computes the cumulative hazard function of the binomial distribution. | NULL | [dist_binomial_chf(10, 0.5, 5)] |
| dist_binomial_hazard | scalar | Computes the hazard function of the binomial distribution. | NULL | [dist_binomial_hazard(10, 0.5, 5)] |
| dist_binomial_kurtosis | scalar | Returns the kurtosis of the binomial distribution. | NULL | [dist_binomial_kurtosis(10, 0.5)] |
| dist_binomial_kurtosis_excess | scalar | Returns the excess kurtosis of the binomial distribution. | NULL | [dist_binomial_kurtosis_excess(10, 0.5)] |
| dist_binomial_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the binomial distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_binomial_log_cdf(10, 0.5, 5)] |
| dist_binomial_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the binomial distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_binomial_log_cdf_complement(10, 0.5, 5)] |
| dist_binomial_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the binomial distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_binomial_log_pdf(10, 0.5, 5)] |
| dist_binomial_median | scalar | Returns the median (50th percentile) of the binomial distribution, which equals the mean. | NULL | [dist_binomial_median(10, 0.5)] |
| dist_binomial_mode | scalar | Returns the mode (most likely value) of the binomial distribution, which equals the mean. | NULL | [dist_binomial_mode(10, 0.5)] |
| dist_binomial_pdf | scalar | Computes the probability density function (PDF) of the binomial distribution. Returns the probability densityat point x for a binomial distribution with specified parameters. | NULL | [dist_binomial_pdf(10, 0.5, 5)] |
| dist_binomial_quantile | scalar | Computes the quantile function (inverse CDF) of the binomial distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_binomial_quantile(10, 0.5, 0.95)] |
| dist_binomial_quantile_complement | scalar | Computes the complementary quantile function of the binomial distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_binomial_quantile_complement(10, 0.5, 0.05)] |
| dist_binomial_range | scalar | Returns the range of the binomial distribution. | NULL | [dist_binomial_range(10, 0.5)] |
| dist_binomial_sample | scalar | Generates random samples from the binomial distribution with specified parameters. | NULL | [dist_binomial_sample(10, 0.5)] |
| dist_binomial_skewness | scalar | Returns the skewness of the binomial distribution. | NULL | [dist_binomial_skewness(10, 0.5)] |
| dist_binomial_support | scalar | Returns the support of the binomial distribution. | NULL | [dist_binomial_support(10, 0.5)] |
| dist_binomial_variance | scalar | Returns the variance (σ²) of the binomial distribution. | NULL | [dist_binomial_variance(10, 0.5)] |
| dist_cauchy_cdf | scalar | Computes the cumulative distribution function (CDF) of the cauchy distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_cauchy_cdf(0, 1.0, 0.5)] |
| dist_cauchy_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the cauchy distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_cauchy_cdf_complement(0, 1.0, 0.5)] |
| dist_cauchy_chf | scalar | Computes the cumulative hazard function of the cauchy distribution. | NULL | [dist_cauchy_chf(0, 1.0, 0.5)] |
| dist_cauchy_hazard | scalar | Computes the hazard function of the cauchy distribution. | NULL | [dist_cauchy_hazard(0, 1.0, 0.5)] |
| dist_cauchy_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the cauchy distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_cauchy_log_cdf(0, 1.0, 0.5)] |
| dist_cauchy_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the cauchy distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_cauchy_log_cdf_complement(0, 1.0, 0.5)] |
| dist_cauchy_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the cauchy distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_cauchy_log_pdf(0, 1.0, 0.5)] |
| dist_cauchy_median | scalar | Returns the median (50th percentile) of the cauchy distribution, which equals the mean. | NULL | [dist_cauchy_median(0.0, 1.0)] |
| dist_cauchy_mode | scalar | Returns the mode (most likely value) of the cauchy distribution, which equals the mean. | NULL | [dist_cauchy_mode(0.0, 1.0)] |
| dist_cauchy_pdf | scalar | Computes the probability density function (PDF) of the cauchy distribution. Returns the probability densityat point x for a cauchy distribution with specified parameters. | NULL | [dist_cauchy_pdf(0, 1.0, 0.5)] |
| dist_cauchy_quantile | scalar | Computes the quantile function (inverse CDF) of the cauchy distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_cauchy_quantile(0, 1.0, 0.95)] |
| dist_cauchy_quantile_complement | scalar | Computes the complementary quantile function of the cauchy distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_cauchy_quantile_complement(0, 1.0, 0.95)] |
| dist_cauchy_range | scalar | Returns the range of the cauchy distribution. | NULL | [dist_cauchy_range(0.0, 1.0)] |
| dist_cauchy_sample | scalar | Generates random samples from the cauchy distribution with specified parameters. | NULL | [dist_cauchy_sample(0.0, 1.0)] |
| dist_cauchy_support | scalar | Returns the support of the cauchy distribution. | NULL | [dist_cauchy_support(0.0, 1.0)] |
| dist_chi_squared_cdf | scalar | Computes the cumulative distribution function (CDF) of the chi_squared distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_chi_squared_cdf(5, 3.0)] |
| dist_chi_squared_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the chi_squared distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_chi_squared_cdf_complement(5, 3.0)] |
| dist_chi_squared_chf | scalar | Computes the cumulative hazard function of the chi_squared distribution. | NULL | [dist_chi_squared_chf(5, 3.0)] |
| dist_chi_squared_hazard | scalar | Computes the hazard function of the chi_squared distribution. | NULL | [dist_chi_squared_hazard(5, 3.0)] |
| dist_chi_squared_kurtosis | scalar | Returns the kurtosis of the chi_squared distribution. | NULL | [dist_chi_squared_kurtosis(5)] |
| dist_chi_squared_kurtosis_excess | scalar | Returns the excess kurtosis of the chi_squared distribution. | NULL | [dist_chi_squared_kurtosis_excess(5)] |
| dist_chi_squared_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the chi_squared distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_chi_squared_log_cdf(5, 3.0)] |
| dist_chi_squared_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the chi_squared distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_chi_squared_log_cdf_complement(5, 3.0)] |
| dist_chi_squared_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the chi_squared distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_chi_squared_log_pdf(5, 3.0)] |
| dist_chi_squared_mean | scalar | Returns the mean (μ) of the chi_squared distribution, which is the first moment. | NULL | [dist_chi_squared_mean(5)] |
| dist_chi_squared_median | scalar | Returns the median (50th percentile) of the chi_squared distribution, which equals the mean. | NULL | [dist_chi_squared_median(5)] |
| dist_chi_squared_mode | scalar | Returns the mode (most likely value) of the chi_squared distribution, which equals the mean. | NULL | [dist_chi_squared_mode(5)] |
| dist_chi_squared_pdf | scalar | Computes the probability density function (PDF) of the chi_squared distribution. Returns the probability densityat point x for a chi_squared distribution with specified parameters. | NULL | [dist_chi_squared_pdf(5, 3.0)] |
| dist_chi_squared_quantile | scalar | Computes the quantile function (inverse CDF) of the chi_squared distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_chi_squared_quantile(5, 0.95)] |
| dist_chi_squared_quantile_complement | scalar | Computes the complementary quantile function of the chi_squared distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_chi_squared_quantile_complement(5, 0.05)] |
| dist_chi_squared_range | scalar | Returns the range of the chi_squared distribution. | NULL | [dist_chi_squared_range(5)] |
| dist_chi_squared_sample | scalar | Generates random samples from the chi_squared distribution with specified parameters. | NULL | [dist_chi_squared_sample(5)] |
| dist_chi_squared_skewness | scalar | Returns the skewness of the chi_squared distribution. | NULL | [dist_chi_squared_skewness(5)] |
| dist_chi_squared_stddev | scalar | Returns the standard deviation (σ) of the chi_squared distribution. | NULL | [dist_chi_squared_stddev(5)] |
| dist_chi_squared_support | scalar | Returns the support of the chi_squared distribution. | NULL | [dist_chi_squared_support(5)] |
| dist_chi_squared_variance | scalar | Returns the variance (σ²) of the chi_squared distribution. | NULL | [dist_chi_squared_variance(5)] |
| dist_exponential_cdf | scalar | Computes the cumulative distribution function (CDF) of the exponential distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_exponential_cdf(1.0, 0.5)] |
| dist_exponential_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the exponential distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_exponential_cdf_complement(1.0, 0.5)] |
| dist_exponential_chf | scalar | Computes the cumulative hazard function of the exponential distribution. | NULL | [dist_exponential_chf(1.0, 0.5)] |
| dist_exponential_hazard | scalar | Computes the hazard function of the exponential distribution. | NULL | [dist_exponential_hazard(1.0, 0.5)] |
| dist_exponential_kurtosis | scalar | Returns the kurtosis of the exponential distribution. | NULL | [dist_exponential_kurtosis(1.0)] |
| dist_exponential_kurtosis_excess | scalar | Returns the excess kurtosis of the exponential distribution. | NULL | [dist_exponential_kurtosis_excess(1.0)] |
| dist_exponential_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the exponential distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_exponential_log_cdf(1.0, 0.5)] |
| dist_exponential_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the exponential distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_exponential_log_cdf_complement(1.0, 0.5)] |
| dist_exponential_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the exponential distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_exponential_log_pdf(1.0, 0.5)] |
| dist_exponential_mean | scalar | Returns the mean (μ) of the exponential distribution, which is the first moment. | NULL | [dist_exponential_mean(1.0)] |
| dist_exponential_median | scalar | Returns the median (50th percentile) of the exponential distribution, which equals the mean. | NULL | [dist_exponential_median(1.0)] |
| dist_exponential_mode | scalar | Returns the mode (most likely value) of the exponential distribution, which equals the mean. | NULL | [dist_exponential_mode(1.0)] |
| dist_exponential_pdf | scalar | Computes the probability density function (PDF) of the exponential distribution. Returns the probability densityat point x for a exponential distribution with specified parameters. | NULL | [dist_exponential_pdf(1.0, 0.5)] |
| dist_exponential_quantile | scalar | Computes the quantile function (inverse CDF) of the exponential distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_exponential_quantile(1.0, 0.95)] |
| dist_exponential_quantile_complement | scalar | Computes the complementary quantile function of the exponential distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_exponential_quantile_complement(1.0, 0.05)] |
| dist_exponential_range | scalar | Returns the range of the exponential distribution. | NULL | [dist_exponential_range(1.0)] |
| dist_exponential_sample | scalar | Generates random samples from the exponential distribution with specified parameters. | NULL | [dist_exponential_sample(1.0)] |
| dist_exponential_skewness | scalar | Returns the skewness of the exponential distribution. | NULL | [dist_exponential_skewness(1.0)] |
| dist_exponential_stddev | scalar | Returns the standard deviation (σ) of the exponential distribution. | NULL | [dist_exponential_stddev(1.0)] |
| dist_exponential_support | scalar | Returns the support of the exponential distribution. | NULL | [dist_exponential_support(1.0)] |
| dist_exponential_variance | scalar | Returns the variance (σ²) of the exponential distribution. | NULL | [dist_exponential_variance(1.0)] |
| dist_extreme_value_cdf | scalar | Computes the cumulative distribution function (CDF) of the extreme_value distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_extreme_value_cdf(0, 1.0, 0.5)] |
| dist_extreme_value_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the extreme_value distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_extreme_value_cdf_complement(0, 1.0, 0.5)] |
| dist_extreme_value_chf | scalar | Computes the cumulative hazard function of the extreme_value distribution. | NULL | [dist_extreme_value_chf(0, 1.0, 0.5)] |
| dist_extreme_value_hazard | scalar | Computes the hazard function of the extreme_value distribution. | NULL | [dist_extreme_value_hazard(0, 1.0, 0.5)] |
| dist_extreme_value_kurtosis | scalar | Returns the kurtosis of the extreme_value distribution. | NULL | [dist_extreme_value_kurtosis(0.0, 1.0)] |
| dist_extreme_value_kurtosis_excess | scalar | Returns the excess kurtosis of the extreme_value distribution. | NULL | [dist_extreme_value_kurtosis_excess(0.0, 1.0)] |
| dist_extreme_value_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the extreme_value distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_extreme_value_log_cdf(0, 1.0, 0.5)] |
| dist_extreme_value_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the extreme_value distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_extreme_value_log_cdf_complement(0, 1.0, 0.5)] |
| dist_extreme_value_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the extreme_value distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_extreme_value_log_pdf(0, 1.0, 0.5)] |
| dist_extreme_value_median | scalar | Returns the median (50th percentile) of the extreme_value distribution, which equals the mean. | NULL | [dist_extreme_value_median(0.0, 1.0)] |
| dist_extreme_value_mode | scalar | Returns the mode (most likely value) of the extreme_value distribution, which equals the mean. | NULL | [dist_extreme_value_mode(0.0, 1.0)] |
| dist_extreme_value_pdf | scalar | Computes the probability density function (PDF) of the extreme_value distribution. Returns the probability densityat point x for a extreme_value distribution with specified parameters. | NULL | [dist_extreme_value_pdf(0, 1.0, 0.5)] |
| dist_extreme_value_quantile | scalar | Computes the quantile function (inverse CDF) of the extreme_value distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_extreme_value_quantile(0, 1.0, 0.95)] |
| dist_extreme_value_quantile_complement | scalar | Computes the complementary quantile function of the extreme_value distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_extreme_value_quantile_complement(0, 1.0, 0.95)] |
| dist_extreme_value_range | scalar | Returns the range of the extreme_value distribution. | NULL | [dist_extreme_value_range(0.0, 1.0)] |
| dist_extreme_value_sample | scalar | Generates random samples from the extreme_value distribution with specified parameters. | NULL | [dist_extreme_value_sample(0.0, 1.0)] |
| dist_extreme_value_skewness | scalar | Returns the skewness of the extreme_value distribution. | NULL | [dist_extreme_value_skewness(0.0, 1.0)] |
| dist_extreme_value_support | scalar | Returns the support of the extreme_value distribution. | NULL | [dist_extreme_value_support(0.0, 1.0)] |
| dist_extreme_value_variance | scalar | Returns the variance (σ²) of the extreme_value distribution. | NULL | [dist_extreme_value_variance(0.0, 1.0)] |
| dist_fisher_f_cdf | scalar | Computes the cumulative distribution function (CDF) of the fisher_f distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_fisher_f_cdf(5, 10, 0.5)] |
| dist_fisher_f_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the fisher_f distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_fisher_f_cdf_complement(5, 10, 0.5)] |
| dist_fisher_f_chf | scalar | Computes the cumulative hazard function of the fisher_f distribution. | NULL | [dist_fisher_f_chf(5, 10, 0.5)] |
| dist_fisher_f_hazard | scalar | Computes the hazard function of the fisher_f distribution. | NULL | [dist_fisher_f_hazard(5, 10, 0.5)] |
| dist_fisher_f_kurtosis | scalar | Returns the kurtosis of the fisher_f distribution. | NULL | [dist_fisher_f_kurtosis(5, 10)] |
| dist_fisher_f_kurtosis_excess | scalar | Returns the excess kurtosis of the fisher_f distribution. | NULL | [dist_fisher_f_kurtosis_excess(5, 10)] |
| dist_fisher_f_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the fisher_f distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_fisher_f_log_cdf(5, 10, 0.5)] |
| dist_fisher_f_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the fisher_f distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_fisher_f_log_cdf_complement(5, 10, 0.5)] |
| dist_fisher_f_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the fisher_f distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_fisher_f_log_pdf(5, 10, 0.5)] |
| dist_fisher_f_median | scalar | Returns the median (50th percentile) of the fisher_f distribution, which equals the mean. | NULL | [dist_fisher_f_median(5, 10)] |
| dist_fisher_f_mode | scalar | Returns the mode (most likely value) of the fisher_f distribution, which equals the mean. | NULL | [dist_fisher_f_mode(5, 10)] |
| dist_fisher_f_pdf | scalar | Computes the probability density function (PDF) of the fisher_f distribution. Returns the probability densityat point x for a fisher_f distribution with specified parameters. | NULL | [dist_fisher_f_pdf(5, 10, 0.5)] |
| dist_fisher_f_quantile | scalar | Computes the quantile function (inverse CDF) of the fisher_f distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_fisher_f_quantile(5, 10, 0.95)] |
| dist_fisher_f_quantile_complement | scalar | Computes the complementary quantile function of the fisher_f distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_fisher_f_quantile_complement(5, 10, 0.05)] |
| dist_fisher_f_range | scalar | Returns the range of the fisher_f distribution. | NULL | [dist_fisher_f_range(5, 10)] |
| dist_fisher_f_sample | scalar | Generates random samples from the fisher_f distribution with specified parameters. | NULL | [dist_fisher_f_sample(5, 10)] |
| dist_fisher_f_skewness | scalar | Returns the skewness of the fisher_f distribution. | NULL | [dist_fisher_f_skewness(5, 10)] |
| dist_fisher_f_support | scalar | Returns the support of the fisher_f distribution. | NULL | [dist_fisher_f_support(5, 10)] |
| dist_fisher_f_variance | scalar | Returns the variance (σ²) of the fisher_f distribution. | NULL | [dist_fisher_f_variance(5, 10)] |
| dist_gamma_cdf | scalar | Computes the cumulative distribution function (CDF) of the gamma distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_gamma_cdf(2.0, 1.0, 1.5)] |
| dist_gamma_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the gamma distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_gamma_cdf_complement(2.0, 1.0, 1.5)] |
| dist_gamma_chf | scalar | Computes the cumulative hazard function of the gamma distribution. | NULL | [dist_gamma_chf(2.0, 1.0, 1.5)] |
| dist_gamma_hazard | scalar | Computes the hazard function of the gamma distribution. | NULL | [dist_gamma_hazard(2.0, 1.0, 1.5)] |
| dist_gamma_kurtosis | scalar | Returns the kurtosis of the gamma distribution. | NULL | [dist_gamma_kurtosis(2.0, 1.0)] |
| dist_gamma_kurtosis_excess | scalar | Returns the excess kurtosis of the gamma distribution. | NULL | [dist_gamma_kurtosis_excess(2.0, 1.0)] |
| dist_gamma_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the gamma distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_gamma_log_cdf(2.0, 1.0, 1.5)] |
| dist_gamma_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the gamma distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_gamma_log_cdf_complement(2.0, 1.0, 1.5)] |
| dist_gamma_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the gamma distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_gamma_log_pdf(2.0, 1.0, 1.5)] |
| dist_gamma_mean | scalar | Returns the mean (μ) of the gamma distribution, which is the first moment. | NULL | [dist_gamma_mean(2.0, 1.0)] |
| dist_gamma_median | scalar | Returns the median (50th percentile) of the gamma distribution, which equals the mean. | NULL | [dist_gamma_median(2.0, 1.0)] |
| dist_gamma_mode | scalar | Returns the mode (most likely value) of the gamma distribution, which equals the mean. | NULL | [dist_gamma_mode(2.0, 1.0)] |
| dist_gamma_pdf | scalar | Computes the probability density function (PDF) of the gamma distribution. Returns the probability densityat point x for a gamma distribution with specified parameters. | NULL | [dist_gamma_pdf(2.0, 1.0, 1.5)] |
| dist_gamma_quantile | scalar | Computes the quantile function (inverse CDF) of the gamma distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_gamma_quantile(2.0, 1.0, 0.95)] |
| dist_gamma_quantile_complement | scalar | Computes the complementary quantile function of the gamma distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_gamma_quantile_complement(2.0, 1.0, 0.05)] |
| dist_gamma_range | scalar | Returns the range of the gamma distribution. | NULL | [dist_gamma_range(2.0, 1.0)] |
| dist_gamma_sample | scalar | Generates random samples from the gamma distribution with specified parameters. | NULL | [dist_gamma_sample(2.0, 1.0)] |
| dist_gamma_skewness | scalar | Returns the skewness of the gamma distribution. | NULL | [dist_gamma_skewness(2.0, 1.0)] |
| dist_gamma_stddev | scalar | Returns the standard deviation (σ) of the gamma distribution. | NULL | [dist_gamma_stddev(2.0, 1.0)] |
| dist_gamma_support | scalar | Returns the support of the gamma distribution. | NULL | [dist_gamma_support(2.0, 1.0)] |
| dist_gamma_variance | scalar | Returns the variance (σ²) of the gamma distribution. | NULL | [dist_gamma_variance(2.0, 1.0)] |
| dist_geometric_cdf | scalar | Computes the cumulative distribution function (CDF) of the geometric distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_geometric_cdf(0.5, 2)] |
| dist_geometric_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the geometric distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_geometric_cdf_complement(0.5, 2)] |
| dist_geometric_chf | scalar | Computes the cumulative hazard function of the geometric distribution. | NULL | [dist_geometric_chf(0.5, 2)] |
| dist_geometric_hazard | scalar | Computes the hazard function of the geometric distribution. | NULL | [dist_geometric_hazard(0.5, 2)] |
| dist_geometric_kurtosis | scalar | Returns the kurtosis of the geometric distribution. | NULL | [dist_geometric_kurtosis(0.5)] |
| dist_geometric_kurtosis_excess | scalar | Returns the excess kurtosis of the geometric distribution. | NULL | [dist_geometric_kurtosis_excess(0.5)] |
| dist_geometric_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the geometric distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_geometric_log_cdf(0.5, 2)] |
| dist_geometric_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the geometric distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_geometric_log_cdf_complement(0.5, 2)] |
| dist_geometric_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the geometric distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_geometric_log_pdf(0.5, 2)] |
| dist_geometric_mean | scalar | Returns the mean (μ) of the geometric distribution, which is the first moment. | NULL | [dist_geometric_mean(0.5)] |
| dist_geometric_median | scalar | Returns the median (50th percentile) of the geometric distribution, which equals the mean. | NULL | [dist_geometric_median(0.5)] |
| dist_geometric_mode | scalar | Returns the mode (most likely value) of the geometric distribution, which equals the mean. | NULL | [dist_geometric_mode(0.5)] |
| dist_geometric_pdf | scalar | Computes the probability density function (PDF) of the geometric distribution. Returns the probability densityat point x for a geometric distribution with specified parameters. | NULL | [dist_geometric_pdf(0.5, 2)] |
| dist_geometric_quantile | scalar | Computes the quantile function (inverse CDF) of the geometric distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_geometric_quantile(0.5, 0.95)] |
| dist_geometric_quantile_complement | scalar | Computes the complementary quantile function of the geometric distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_geometric_quantile_complement(0.5, 0.05)] |
| dist_geometric_range | scalar | Returns the range of the geometric distribution. | NULL | [dist_geometric_range(0.5)] |
| dist_geometric_sample | scalar | Generates random samples from the geometric distribution with specified parameters. | NULL | [dist_geometric_sample(0.5)] |
| dist_geometric_skewness | scalar | Returns the skewness of the geometric distribution. | NULL | [dist_geometric_skewness(0.5)] |
| dist_geometric_stddev | scalar | Returns the standard deviation (σ) of the geometric distribution. | NULL | [dist_geometric_stddev(0.5)] |
| dist_geometric_support | scalar | Returns the support of the geometric distribution. | NULL | [dist_geometric_support(0.5)] |
| dist_geometric_variance | scalar | Returns the variance (σ²) of the geometric distribution. | NULL | [dist_geometric_variance(0.5)] |
| dist_laplace_cdf | scalar | Computes the cumulative distribution function (CDF) of the laplace distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_laplace_cdf(0, 1.0, 0.5)] |
| dist_laplace_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the laplace distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_laplace_cdf_complement(0, 1.0, 0.5)] |
| dist_laplace_chf | scalar | Computes the cumulative hazard function of the laplace distribution. | NULL | [dist_laplace_chf(0, 1.0, 0.5)] |
| dist_laplace_hazard | scalar | Computes the hazard function of the laplace distribution. | NULL | [dist_laplace_hazard(0, 1.0, 0.5)] |
| dist_laplace_kurtosis | scalar | Returns the kurtosis of the laplace distribution. | NULL | [dist_laplace_kurtosis(0.0, 1.0)] |
| dist_laplace_kurtosis_excess | scalar | Returns the excess kurtosis of the laplace distribution. | NULL | [dist_laplace_kurtosis_excess(0.0, 1.0)] |
| dist_laplace_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the laplace distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_laplace_log_cdf(0, 1.0, 0.5)] |
| dist_laplace_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the laplace distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_laplace_log_cdf_complement(0, 1.0, 0.5)] |
| dist_laplace_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the laplace distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_laplace_log_pdf(0, 1.0, 0.5)] |
| dist_laplace_mean | scalar | Returns the mean (μ) of the laplace distribution, which is the first moment. | NULL | [dist_laplace_mean(0.0, 1.0)] |
| dist_laplace_median | scalar | Returns the median (50th percentile) of the laplace distribution, which equals the mean. | NULL | [dist_laplace_median(0.0, 1.0)] |
| dist_laplace_mode | scalar | Returns the mode (most likely value) of the laplace distribution, which equals the mean. | NULL | [dist_laplace_mode(0.0, 1.0)] |
| dist_laplace_pdf | scalar | Computes the probability density function (PDF) of the laplace distribution. Returns the probability densityat point x for a laplace distribution with specified parameters. | NULL | [dist_laplace_pdf(0, 1.0, 0.5)] |
| dist_laplace_quantile | scalar | Computes the quantile function (inverse CDF) of the laplace distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_laplace_quantile(0, 1.0, 0.95)] |
| dist_laplace_quantile_complement | scalar | Computes the complementary quantile function of the laplace distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_laplace_quantile_complement(0, 1.0, 0.95)] |
| dist_laplace_range | scalar | Returns the range of the laplace distribution. | NULL | [dist_laplace_range(0.0, 1.0)] |
| dist_laplace_sample | scalar | Generates random samples from the laplace distribution with specified parameters. | NULL | [dist_laplace_sample(0.0, 1.0)] |
| dist_laplace_skewness | scalar | Returns the skewness of the laplace distribution. | NULL | [dist_laplace_skewness(0.0, 1.0)] |
| dist_laplace_stddev | scalar | Returns the standard deviation (σ) of the laplace distribution. | NULL | [dist_laplace_stddev(0.0, 1.0)] |
| dist_laplace_support | scalar | Returns the support of the laplace distribution. | NULL | [dist_laplace_support(0.0, 1.0)] |
| dist_laplace_variance | scalar | Returns the variance (σ²) of the laplace distribution. | NULL | [dist_laplace_variance(0.0, 1.0)] |
| dist_logistic_cdf | scalar | Computes the cumulative distribution function (CDF) of the logistic distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_logistic_cdf(0, 1.0, 0.5)] |
| dist_logistic_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the logistic distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_logistic_cdf_complement(0, 1.0, 0.5)] |
| dist_logistic_chf | scalar | Computes the cumulative hazard function of the logistic distribution. | NULL | [dist_logistic_chf(0, 1.0, 0.5)] |
| dist_logistic_hazard | scalar | Computes the hazard function of the logistic distribution. | NULL | [dist_logistic_hazard(0, 1.0, 0.5)] |
| dist_logistic_kurtosis | scalar | Returns the kurtosis of the logistic distribution. | NULL | [dist_logistic_kurtosis(0.0, 1.0)] |
| dist_logistic_kurtosis_excess | scalar | Returns the excess kurtosis of the logistic distribution. | NULL | [dist_logistic_kurtosis_excess(0.0, 1.0)] |
| dist_logistic_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the logistic distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_logistic_log_cdf(0, 1.0, 0.5)] |
| dist_logistic_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the logistic distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_logistic_log_cdf_complement(0, 1.0, 0.5)] |
| dist_logistic_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the logistic distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_logistic_log_pdf(0, 1.0, 0.5)] |
| dist_logistic_median | scalar | Returns the median (50th percentile) of the logistic distribution, which equals the mean. | NULL | [dist_logistic_median(0.0, 1.0)] |
| dist_logistic_mode | scalar | Returns the mode (most likely value) of the logistic distribution, which equals the mean. | NULL | [dist_logistic_mode(0.0, 1.0)] |
| dist_logistic_pdf | scalar | Computes the probability density function (PDF) of the logistic distribution. Returns the probability densityat point x for a logistic distribution with specified parameters. | NULL | [dist_logistic_pdf(0, 1.0, 0.5)] |
| dist_logistic_quantile | scalar | Computes the quantile function (inverse CDF) of the logistic distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_logistic_quantile(0, 1.0, 0.95)] |
| dist_logistic_quantile_complement | scalar | Computes the complementary quantile function of the logistic distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_logistic_quantile_complement(0, 1.0, 0.95)] |
| dist_logistic_range | scalar | Returns the range of the logistic distribution. | NULL | [dist_logistic_range(0.0, 1.0)] |
| dist_logistic_sample | scalar | Generates random samples from the logistic distribution with specified parameters. | NULL | [dist_logistic_sample(0.0, 1.0)] |
| dist_logistic_skewness | scalar | Returns the skewness of the logistic distribution. | NULL | [dist_logistic_skewness(0.0, 1.0)] |
| dist_logistic_support | scalar | Returns the support of the logistic distribution. | NULL | [dist_logistic_support(0.0, 1.0)] |
| dist_logistic_variance | scalar | Returns the variance (σ²) of the logistic distribution. | NULL | [dist_logistic_variance(0.0, 1.0)] |
| dist_lognormal_cdf | scalar | Computes the cumulative distribution function (CDF) of the lognormal distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_lognormal_cdf(0, 1.0, 0.5)] |
| dist_lognormal_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the lognormal distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_lognormal_cdf_complement(0, 1.0, 0.5)] |
| dist_lognormal_chf | scalar | Computes the cumulative hazard function of the lognormal distribution. | NULL | [dist_lognormal_chf(0, 1.0, 0.5)] |
| dist_lognormal_hazard | scalar | Computes the hazard function of the lognormal distribution. | NULL | [dist_lognormal_hazard(0, 1.0, 0.5)] |
| dist_lognormal_kurtosis | scalar | Returns the kurtosis of the lognormal distribution. | NULL | [dist_lognormal_kurtosis(0.0, 1.0)] |
| dist_lognormal_kurtosis_excess | scalar | Returns the excess kurtosis of the lognormal distribution. | NULL | [dist_lognormal_kurtosis_excess(0.0, 1.0)] |
| dist_lognormal_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the lognormal distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_lognormal_log_cdf(0, 1.0, 0.5)] |
| dist_lognormal_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the lognormal distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_lognormal_log_cdf_complement(0, 1.0, 0.5)] |
| dist_lognormal_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the lognormal distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_lognormal_log_pdf(0, 1.0, 0.5)] |
| dist_lognormal_mean | scalar | Returns the mean (μ) of the lognormal distribution, which is the first moment. | NULL | [dist_lognormal_mean(0.0, 1.0)] |
| dist_lognormal_median | scalar | Returns the median (50th percentile) of the lognormal distribution, which equals the mean. | NULL | [dist_lognormal_median(0.0, 1.0)] |
| dist_lognormal_mode | scalar | Returns the mode (most likely value) of the lognormal distribution, which equals the mean. | NULL | [dist_lognormal_mode(0.0, 1.0)] |
| dist_lognormal_pdf | scalar | Computes the probability density function (PDF) of the lognormal distribution. Returns the probability densityat point x for a lognormal distribution with specified parameters. | NULL | [dist_lognormal_pdf(0, 1.0, 0.5)] |
| dist_lognormal_quantile | scalar | Computes the quantile function (inverse CDF) of the lognormal distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_lognormal_quantile(0, 1.0, 0.95)] |
| dist_lognormal_quantile_complement | scalar | Computes the complementary quantile function of the lognormal distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_lognormal_quantile_complement(0, 1.0, 0.95)] |
| dist_lognormal_range | scalar | Returns the range of the lognormal distribution. | NULL | [dist_lognormal_range(0.0, 1.0)] |
| dist_lognormal_sample | scalar | Generates random samples from the lognormal distribution with specified parameters. | NULL | [dist_lognormal_sample(0.0, 1.0)] |
| dist_lognormal_skewness | scalar | Returns the skewness of the lognormal distribution. | NULL | [dist_lognormal_skewness(0.0, 1.0)] |
| dist_lognormal_stddev | scalar | Returns the standard deviation (σ) of the lognormal distribution. | NULL | [dist_lognormal_stddev(0.0, 1.0)] |
| dist_lognormal_support | scalar | Returns the support of the lognormal distribution. | NULL | [dist_lognormal_support(0.0, 1.0)] |
| dist_lognormal_variance | scalar | Returns the variance (σ²) of the lognormal distribution. | NULL | [dist_lognormal_variance(0.0, 1.0)] |
| dist_negative_binomial_cdf | scalar | Computes the cumulative distribution function (CDF) of the negative_binomial distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_negative_binomial_cdf(10, 0.5, 5)] |
| dist_negative_binomial_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the negative_binomial distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_negative_binomial_cdf_complement(10, 0.5, 5)] |
| dist_negative_binomial_chf | scalar | Computes the cumulative hazard function of the negative_binomial distribution. | NULL | [dist_negative_binomial_chf(10, 0.5, 5)] |
| dist_negative_binomial_hazard | scalar | Computes the hazard function of the negative_binomial distribution. | NULL | [dist_negative_binomial_hazard(10, 0.5, 5)] |
| dist_negative_binomial_kurtosis | scalar | Returns the kurtosis of the negative_binomial distribution. | NULL | [dist_negative_binomial_kurtosis(10, 0.5)] |
| dist_negative_binomial_kurtosis_excess | scalar | Returns the excess kurtosis of the negative_binomial distribution. | NULL | [dist_negative_binomial_kurtosis_excess(10, 0.5)] |
| dist_negative_binomial_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the negative_binomial distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_negative_binomial_log_cdf(10, 0.5, 5)] |
| dist_negative_binomial_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the negative_binomial distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_negative_binomial_log_cdf_complement(10, 0.5, 5)] |
| dist_negative_binomial_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the negative_binomial distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_negative_binomial_log_pdf(10, 0.5, 5)] |
| dist_negative_binomial_median | scalar | Returns the median (50th percentile) of the negative_binomial distribution, which equals the mean. | NULL | [dist_negative_binomial_median(10, 0.5)] |
| dist_negative_binomial_mode | scalar | Returns the mode (most likely value) of the negative_binomial distribution, which equals the mean. | NULL | [dist_negative_binomial_mode(10, 0.5)] |
| dist_negative_binomial_pdf | scalar | Computes the probability density function (PDF) of the negative_binomial distribution. Returns the probability densityat point x for a negative_binomial distribution with specified parameters. | NULL | [dist_negative_binomial_pdf(10, 0.5, 5)] |
| dist_negative_binomial_quantile | scalar | Computes the quantile function (inverse CDF) of the negative_binomial distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_negative_binomial_quantile(10, 0.5, 0.95)] |
| dist_negative_binomial_quantile_complement | scalar | Computes the complementary quantile function of the negative_binomial distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_negative_binomial_quantile_complement(10, 0.5, 0.05)] |
| dist_negative_binomial_range | scalar | Returns the range of the negative_binomial distribution. | NULL | [dist_negative_binomial_range(10, 0.5)] |
| dist_negative_binomial_sample | scalar | Generates random samples from the negative_binomial distribution with specified parameters. | NULL | [dist_negative_binomial_sample(10, 0.5)] |
| dist_negative_binomial_skewness | scalar | Returns the skewness of the negative_binomial distribution. | NULL | [dist_negative_binomial_skewness(10, 0.5)] |
| dist_negative_binomial_support | scalar | Returns the support of the negative_binomial distribution. | NULL | [dist_negative_binomial_support(10, 0.5)] |
| dist_negative_binomial_variance | scalar | Returns the variance (σ²) of the negative_binomial distribution. | NULL | [dist_negative_binomial_variance(10, 0.5)] |
| dist_normal_cdf | scalar | Computes the cumulative distribution function (CDF) of the normal distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_normal_cdf(0, 1.0, 0.5)] |
| dist_normal_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the normal distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_normal_cdf_complement(0, 1.0, 0.5)] |
| dist_normal_chf | scalar | Computes the cumulative hazard function of the normal distribution. | NULL | [dist_normal_chf(0, 1.0, 0.5)] |
| dist_normal_hazard | scalar | Computes the hazard function of the normal distribution. | NULL | [dist_normal_hazard(0, 1.0, 0.5)] |
| dist_normal_kurtosis | scalar | Returns the kurtosis of the normal distribution. | NULL | [dist_normal_kurtosis(0.0, 1.0)] |
| dist_normal_kurtosis_excess | scalar | Returns the excess kurtosis of the normal distribution. | NULL | [dist_normal_kurtosis_excess(0.0, 1.0)] |
| dist_normal_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the normal distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_normal_log_cdf(0, 1.0, 0.5)] |
| dist_normal_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the normal distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_normal_log_cdf_complement(0, 1.0, 0.5)] |
| dist_normal_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the normal distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_normal_log_pdf(0, 1.0, 0.5)] |
| dist_normal_mean | scalar | Returns the mean (μ) of the normal distribution, which is the first moment. | NULL | [dist_normal_mean(0.0, 1.0)] |
| dist_normal_median | scalar | Returns the median (50th percentile) of the normal distribution, which equals the mean. | NULL | [dist_normal_median(0.0, 1.0)] |
| dist_normal_mode | scalar | Returns the mode (most likely value) of the normal distribution, which equals the mean. | NULL | [dist_normal_mode(0.0, 1.0)] |
| dist_normal_pdf | scalar | Computes the probability density function (PDF) of the normal distribution. Returns the probability densityat point x for a normal distribution with specified parameters. | NULL | [dist_normal_pdf(0, 1.0, 0.5)] |
| dist_normal_quantile | scalar | Computes the quantile function (inverse CDF) of the normal distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_normal_quantile(0, 1.0, 0.95)] |
| dist_normal_quantile_complement | scalar | Computes the complementary quantile function of the normal distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_normal_quantile_complement(0, 1.0, 0.95)] |
| dist_normal_range | scalar | Returns the range of the normal distribution. | NULL | [dist_normal_range(0.0, 1.0)] |
| dist_normal_sample | scalar | Generates random samples from the normal distribution with specified parameters. | NULL | [dist_normal_sample(0.0, 1.0)] |
| dist_normal_skewness | scalar | Returns the skewness of the normal distribution. | NULL | [dist_normal_skewness(0.0, 1.0)] |
| dist_normal_stddev | scalar | Returns the standard deviation (σ) of the normal distribution. | NULL | [dist_normal_stddev(0.0, 1.0)] |
| dist_normal_support | scalar | Returns the support of the normal distribution. | NULL | [dist_normal_support(0.0, 1.0)] |
| dist_normal_variance | scalar | Returns the variance (σ²) of the normal distribution. | NULL | [dist_normal_variance(0.0, 1.0)] |
| dist_pareto_cdf | scalar | Computes the cumulative distribution function (CDF) of the pareto distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_pareto_cdf(1.0, 3.0, 1.5)] |
| dist_pareto_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the pareto distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_pareto_cdf_complement(1.0, 3.0, 1.5)] |
| dist_pareto_chf | scalar | Computes the cumulative hazard function of the pareto distribution. | NULL | [dist_pareto_chf(1.0, 3.0, 1.5)] |
| dist_pareto_hazard | scalar | Computes the hazard function of the pareto distribution. | NULL | [dist_pareto_hazard(1.0, 3.0, 1.5)] |
| dist_pareto_kurtosis | scalar | Returns the kurtosis of the pareto distribution. | NULL | [dist_pareto_kurtosis(1.0, 5.0)] |
| dist_pareto_kurtosis_excess | scalar | Returns the excess kurtosis of the pareto distribution. | NULL | [dist_pareto_kurtosis_excess(1.0, 5.0)] |
| dist_pareto_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the pareto distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_pareto_log_cdf(1.0, 3.0, 1.5)] |
| dist_pareto_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the pareto distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_pareto_log_cdf_complement(1.0, 3.0, 1.5)] |
| dist_pareto_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the pareto distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_pareto_log_pdf(1.0, 3.0, 1.5)] |
| dist_pareto_mean | scalar | Returns the mean (μ) of the pareto distribution, which is the first moment. | NULL | [dist_pareto_mean(1.0, 3.0)] |
| dist_pareto_median | scalar | Returns the median (50th percentile) of the pareto distribution. | NULL | [dist_pareto_median(1.0, 3.0)] |
| dist_pareto_mode | scalar | Returns the mode of the pareto distribution, which equals the scale (minimum). | NULL | [dist_pareto_mode(1.0, 3.0)] |
| dist_pareto_pdf | scalar | Computes the probability density function (PDF) of the pareto distribution. Returns the probability densityat point x for a pareto distribution with specified parameters. | NULL | [dist_pareto_pdf(1.0, 3.0, 1.5)] |
| dist_pareto_quantile | scalar | Computes the quantile function (inverse CDF) of the pareto distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_pareto_quantile(1.0, 3.0, 0.95)] |
| dist_pareto_quantile_complement | scalar | Computes the complementary quantile function of the pareto distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_pareto_quantile_complement(1.0, 3.0, 0.05)] |
| dist_pareto_range | scalar | Returns the range of the pareto distribution. | NULL | [dist_pareto_range(1.0, 3.0)] |
| dist_pareto_sample | scalar | Generates random samples from the pareto distribution with specified parameters. | NULL | [dist_pareto_sample(1.0, 3.0)] |
| dist_pareto_skewness | scalar | Returns the skewness of the pareto distribution. | NULL | [dist_pareto_skewness(1.0, 5.0)] |
| dist_pareto_stddev | scalar | Returns the standard deviation (σ) of the pareto distribution. | NULL | [dist_pareto_stddev(1.0, 3.0)] |
| dist_pareto_support | scalar | Returns the support of the pareto distribution. | NULL | [dist_pareto_support(1.0, 3.0)] |
| dist_pareto_variance | scalar | Returns the variance (σ²) of the pareto distribution. | NULL | [dist_pareto_variance(1.0, 3.0)] |
| dist_poisson_cdf | scalar | Computes the cumulative distribution function (CDF) of the poisson distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_poisson_cdf(5.0, 3)] |
| dist_poisson_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the poisson distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_poisson_cdf_complement(5.0, 3)] |
| dist_poisson_chf | scalar | Computes the cumulative hazard function of the poisson distribution. | NULL | [dist_poisson_chf(5.0, 3)] |
| dist_poisson_hazard | scalar | Computes the hazard function of the poisson distribution. | NULL | [dist_poisson_hazard(5.0, 3)] |
| dist_poisson_kurtosis | scalar | Returns the kurtosis of the poisson distribution. | NULL | [dist_poisson_kurtosis(5.0)] |
| dist_poisson_kurtosis_excess | scalar | Returns the excess kurtosis of the poisson distribution. | NULL | [dist_poisson_kurtosis_excess(5.0)] |
| dist_poisson_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the poisson distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_poisson_log_cdf(5.0, 3)] |
| dist_poisson_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the poisson distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_poisson_log_cdf_complement(5.0, 3)] |
| dist_poisson_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the poisson distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_poisson_log_pdf(5.0, 3)] |
| dist_poisson_mean | scalar | Returns the mean (μ) of the poisson distribution, which is the first moment. | NULL | [dist_poisson_mean(5.0)] |
| dist_poisson_median | scalar | Returns the median (50th percentile) of the poisson distribution, which equals the mean. | NULL | [dist_poisson_median(5.0)] |
| dist_poisson_mode | scalar | Returns the mode (most likely value) of the poisson distribution, which equals the mean. | NULL | [dist_poisson_mode(5.0)] |
| dist_poisson_pdf | scalar | Computes the probability density function (PDF) of the poisson distribution. Returns the probability densityat point x for a poisson distribution with specified parameters. | NULL | [dist_poisson_pdf(5.0, 3)] |
| dist_poisson_quantile | scalar | Computes the quantile function (inverse CDF) of the poisson distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_poisson_quantile(5.0, 0.95)] |
| dist_poisson_quantile_complement | scalar | Computes the complementary quantile function of the poisson distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_poisson_quantile_complement(5.0, 0.05)] |
| dist_poisson_range | scalar | Returns the range of the poisson distribution. | NULL | [dist_poisson_range(5.0)] |
| dist_poisson_sample | scalar | Generates random samples from the poisson distribution with specified parameters. | NULL | [dist_poisson_sample(5.0)] |
| dist_poisson_skewness | scalar | Returns the skewness of the poisson distribution. | NULL | [dist_poisson_skewness(5.0)] |
| dist_poisson_stddev | scalar | Returns the standard deviation (σ) of the poisson distribution. | NULL | [dist_poisson_stddev(5.0)] |
| dist_poisson_support | scalar | Returns the support of the poisson distribution. | NULL | [dist_poisson_support(5.0)] |
| dist_poisson_variance | scalar | Returns the variance (σ²) of the poisson distribution. | NULL | [dist_poisson_variance(5.0)] |
| dist_rayleigh_cdf | scalar | Computes the cumulative distribution function (CDF) of the rayleigh distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_rayleigh_cdf(1.0, 0.5)] |
| dist_rayleigh_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the rayleigh distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_rayleigh_cdf_complement(1.0, 0.5)] |
| dist_rayleigh_chf | scalar | Computes the cumulative hazard function of the rayleigh distribution. | NULL | [dist_rayleigh_chf(1.0, 0.5)] |
| dist_rayleigh_hazard | scalar | Computes the hazard function of the rayleigh distribution. | NULL | [dist_rayleigh_hazard(1.0, 0.5)] |
| dist_rayleigh_kurtosis | scalar | Returns the kurtosis of the rayleigh distribution. | NULL | [dist_rayleigh_kurtosis(1.0)] |
| dist_rayleigh_kurtosis_excess | scalar | Returns the excess kurtosis of the rayleigh distribution. | NULL | [dist_rayleigh_kurtosis_excess(1.0)] |
| dist_rayleigh_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the rayleigh distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_rayleigh_log_cdf(1.0, 0.5)] |
| dist_rayleigh_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the rayleigh distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_rayleigh_log_cdf_complement(1.0, 0.5)] |
| dist_rayleigh_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the rayleigh distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_rayleigh_log_pdf(1.0, 0.5)] |
| dist_rayleigh_mean | scalar | Returns the mean (μ) of the rayleigh distribution, which is the first moment. | NULL | [dist_rayleigh_mean(1.0)] |
| dist_rayleigh_median | scalar | Returns the median (50th percentile) of the rayleigh distribution, which equals the mean. | NULL | [dist_rayleigh_median(1.0)] |
| dist_rayleigh_mode | scalar | Returns the mode (most likely value) of the rayleigh distribution, which equals the mean. | NULL | [dist_rayleigh_mode(1.0)] |
| dist_rayleigh_pdf | scalar | Computes the probability density function (PDF) of the rayleigh distribution. Returns the probability densityat point x for a rayleigh distribution with specified parameters. | NULL | [dist_rayleigh_pdf(1.0, 0.5)] |
| dist_rayleigh_quantile | scalar | Computes the quantile function (inverse CDF) of the rayleigh distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_rayleigh_quantile(1.0, 0.95)] |
| dist_rayleigh_quantile_complement | scalar | Computes the complementary quantile function of the rayleigh distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_rayleigh_quantile_complement(1.0, 0.05)] |
| dist_rayleigh_range | scalar | Returns the range of the rayleigh distribution. | NULL | [dist_rayleigh_range(1.0)] |
| dist_rayleigh_sample | scalar | Generates random samples from the rayleigh distribution with specified parameters. | NULL | [dist_rayleigh_sample(1.0)] |
| dist_rayleigh_skewness | scalar | Returns the skewness of the rayleigh distribution. | NULL | [dist_rayleigh_skewness(1.0)] |
| dist_rayleigh_stddev | scalar | Returns the standard deviation (σ) of the rayleigh distribution. | NULL | [dist_rayleigh_stddev(1.0)] |
| dist_rayleigh_support | scalar | Returns the support of the rayleigh distribution. | NULL | [dist_rayleigh_support(1.0)] |
| dist_rayleigh_variance | scalar | Returns the variance (σ²) of the rayleigh distribution. | NULL | [dist_rayleigh_variance(1.0)] |
| dist_students_t_cdf | scalar | Computes the cumulative distribution function (CDF) of the students_t distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_students_t_cdf(10, 1.5)] |
| dist_students_t_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the students_t distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_students_t_cdf_complement(10, 1.5)] |
| dist_students_t_chf | scalar | Computes the cumulative hazard function of the students_t distribution. | NULL | [dist_students_t_chf(10, 1.5)] |
| dist_students_t_hazard | scalar | Computes the hazard function of the students_t distribution. | NULL | [dist_students_t_hazard(10, 1.5)] |
| dist_students_t_kurtosis | scalar | Returns the kurtosis of the students_t distribution. | NULL | [dist_students_t_kurtosis(10)] |
| dist_students_t_kurtosis_excess | scalar | Returns the excess kurtosis of the students_t distribution. | NULL | [dist_students_t_kurtosis_excess(10)] |
| dist_students_t_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the students_t distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_students_t_log_cdf(10, 1.5)] |
| dist_students_t_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the students_t distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_students_t_log_cdf_complement(10, 1.5)] |
| dist_students_t_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the students_t distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_students_t_log_pdf(10, 1.5)] |
| dist_students_t_mean | scalar | Returns the mean (μ) of the students_t distribution, which is the first moment. | NULL | [dist_students_t_mean(10)] |
| dist_students_t_median | scalar | Returns the median (50th percentile) of the students_t distribution, which equals the mean. | NULL | [dist_students_t_median(10)] |
| dist_students_t_mode | scalar | Returns the mode (most likely value) of the students_t distribution, which equals the mean. | NULL | [dist_students_t_mode(10)] |
| dist_students_t_pdf | scalar | Computes the probability density function (PDF) of the students_t distribution. Returns the probability densityat point x for a students_t distribution with specified parameters. | NULL | [dist_students_t_pdf(10, 1.5)] |
| dist_students_t_quantile | scalar | Computes the quantile function (inverse CDF) of the students_t distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_students_t_quantile(10, 0.95)] |
| dist_students_t_quantile_complement | scalar | Computes the complementary quantile function of the students_t distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_students_t_quantile_complement(10, 0.05)] |
| dist_students_t_range | scalar | Returns the range of the students_t distribution. | NULL | [dist_students_t_range(10)] |
| dist_students_t_sample | scalar | Generates random samples from the students_t distribution with specified parameters. | NULL | [dist_students_t_sample(10)] |
| dist_students_t_skewness | scalar | Returns the skewness of the students_t distribution. | NULL | [dist_students_t_skewness(10)] |
| dist_students_t_stddev | scalar | Returns the standard deviation (σ) of the students_t distribution. | NULL | [dist_students_t_stddev(10)] |
| dist_students_t_support | scalar | Returns the support of the students_t distribution. | NULL | [dist_students_t_support(10)] |
| dist_students_t_variance | scalar | Returns the variance (σ²) of the students_t distribution. | NULL | [dist_students_t_variance(10)] |
| dist_uniform_int_cdf | scalar | Computes the cumulative distribution function (CDF) of the uniform_int distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_uniform_int_cdf(1, 6, 3)] |
| dist_uniform_int_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the uniform_int distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_uniform_int_cdf_complement(1, 6, 3)] |
| dist_uniform_int_chf | scalar | Computes the cumulative hazard function of the uniform_int distribution. | NULL | [dist_uniform_int_chf(1, 6, 3)] |
| dist_uniform_int_hazard | scalar | Computes the discrete hazard P(X = x) / P(X >= x). Undefined above max. | NULL | [dist_uniform_int_hazard(1, 6, 3)] |
| dist_uniform_int_kurtosis | scalar | Returns the kurtosis of the uniform_int distribution. | NULL | [dist_uniform_int_kurtosis(1, 6)] |
| dist_uniform_int_kurtosis_excess | scalar | Returns the excess kurtosis of the uniform_int distribution. | NULL | [dist_uniform_int_kurtosis_excess(1, 6)] |
| dist_uniform_int_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the uniform_int distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_uniform_int_log_cdf(1, 6, 3)] |
| dist_uniform_int_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the uniform_int distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_uniform_int_log_cdf_complement(1, 6, 3)] |
| dist_uniform_int_log_pdf | scalar | Computes the natural logarithm of the probability mass function (log-PMF) of the uniform_int distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_uniform_int_log_pdf(1, 6, 3)] |
| dist_uniform_int_mean | scalar | Returns the mean (μ) of the uniform_int distribution, which is the first moment. | NULL | [dist_uniform_int_mean(1, 6)] |
| dist_uniform_int_median | scalar | Returns the median (50th percentile) of the uniform_int distribution, which equals the mean. | NULL | [dist_uniform_int_median(1, 6)] |
| dist_uniform_int_mode | scalar | Returns min as a representative mode; every integer in the support has equal mass. | NULL | [dist_uniform_int_mode(1, 6)] |
| dist_uniform_int_pdf | scalar | Computes the probability mass function (PMF) of the uniform_int distribution. Returns P(X = x) on the inclusive integer support for a uniform_int distribution with specified parameters. | NULL | [dist_uniform_int_pdf(1, 6, 3)] |
| dist_uniform_int_quantile | scalar | Computes the quantile function (inverse CDF) of the uniform_int distribution. Returns the value x with P(X <= x) >= p, using the exact binary DOUBLE probability. At p = 0, returns min. | NULL | [dist_uniform_int_quantile(1, 6, 0.95)] |
| dist_uniform_int_quantile_complement | scalar | Computes the complementary quantile function of the uniform_int distribution. Returns the value x with P(X > x) <= p, using the exact binary DOUBLE probability. At p = 1, returns min. | NULL | [dist_uniform_int_quantile_complement(1, 6, 0.05)] |
| dist_uniform_int_range | scalar | Returns the range of the uniform_int distribution. | NULL | [dist_uniform_int_range(1, 6)] |
| dist_uniform_int_sample | scalar | Generates random samples from the uniform_int distribution with specified parameters. | NULL | [dist_uniform_int_sample(1, 6)] |
| dist_uniform_int_skewness | scalar | Returns the skewness of the uniform_int distribution. | NULL | [dist_uniform_int_skewness(1, 6)] |
| dist_uniform_int_stddev | scalar | Returns the standard deviation (σ) of the uniform_int distribution. | NULL | [dist_uniform_int_stddev(1, 6)] |
| dist_uniform_int_support | scalar | Returns the support of the uniform_int distribution. | NULL | [dist_uniform_int_support(1, 6)] |
| dist_uniform_int_variance | scalar | Returns the variance (σ²) of the uniform_int distribution. | NULL | [dist_uniform_int_variance(1, 6)] |
| dist_uniform_real_cdf | scalar | Computes the cumulative distribution function (CDF) of the uniform_real distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_uniform_real_cdf(0, 1.0, 0.5)] |
| dist_uniform_real_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the uniform_real distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_uniform_real_cdf_complement(0, 1.0, 0.5)] |
| dist_uniform_real_chf | scalar | Computes the cumulative hazard function of the uniform_real distribution. | NULL | [dist_uniform_real_chf(0, 1.0, 0.5)] |
| dist_uniform_real_hazard | scalar | Computes the hazard function of the uniform_real distribution. | NULL | [dist_uniform_real_hazard(0, 1.0, 0.5)] |
| dist_uniform_real_kurtosis | scalar | Returns the kurtosis of the uniform_real distribution. | NULL | [dist_uniform_real_kurtosis(0.0, 1.0)] |
| dist_uniform_real_kurtosis_excess | scalar | Returns the excess kurtosis of the uniform_real distribution. | NULL | [dist_uniform_real_kurtosis_excess(0.0, 1.0)] |
| dist_uniform_real_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the uniform_real distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_uniform_real_log_cdf(0, 1.0, 0.5)] |
| dist_uniform_real_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the uniform_real distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_uniform_real_log_cdf_complement(0, 1.0, 0.5)] |
| dist_uniform_real_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the uniform_real distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_uniform_real_log_pdf(0, 1.0, 0.5)] |
| dist_uniform_real_mean | scalar | Returns the mean (μ) of the uniform_real distribution, which is the first moment. | NULL | [dist_uniform_real_mean(0.0, 1.0)] |
| dist_uniform_real_median | scalar | Returns the median (50th percentile) of the uniform_real distribution, which equals the mean. | NULL | [dist_uniform_real_median(0.0, 1.0)] |
| dist_uniform_real_mode | scalar | Returns the mode (most likely value) of the uniform_real distribution, which equals the mean. | NULL | [dist_uniform_real_mode(0.0, 1.0)] |
| dist_uniform_real_pdf | scalar | Computes the probability density function (PDF) of the uniform_real distribution. Returns the probability densityat point x for a uniform_real distribution with specified parameters. | NULL | [dist_uniform_real_pdf(0, 1.0, 0.5)] |
| dist_uniform_real_quantile | scalar | Computes the quantile function (inverse CDF) of the uniform_real distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_uniform_real_quantile(0, 1.0, 0.95)] |
| dist_uniform_real_quantile_complement | scalar | Computes the complementary quantile function of the uniform_real distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_uniform_real_quantile_complement(0, 1.0, 0.95)] |
| dist_uniform_real_range | scalar | Returns the range of the uniform_real distribution. | NULL | [dist_uniform_real_range(0.0, 1.0)] |
| dist_uniform_real_sample | scalar | Generates random samples from the uniform_real distribution with specified parameters. | NULL | [dist_uniform_real_sample(0.0, 1.0)] |
| dist_uniform_real_skewness | scalar | Returns the skewness of the uniform_real distribution. | NULL | [dist_uniform_real_skewness(0.0, 1.0)] |
| dist_uniform_real_stddev | scalar | Returns the standard deviation (σ) of the uniform_real distribution. | NULL | [dist_uniform_real_stddev(0.0, 1.0)] |
| dist_uniform_real_support | scalar | Returns the support of the uniform_real distribution. | NULL | [dist_uniform_real_support(0.0, 1.0)] |
| dist_uniform_real_variance | scalar | Returns the variance (σ²) of the uniform_real distribution. | NULL | [dist_uniform_real_variance(0.0, 1.0)] |
| dist_weibull_cdf | scalar | Computes the cumulative distribution function (CDF) of the weibull distribution. Returns the probability that a random variable X is less than or equal to x. | NULL | [dist_weibull_cdf(1.5, 1.0, 0.5)] |
| dist_weibull_cdf_complement | scalar | Computes the complementary cumulative distribution function (1 - CDF) of the weibull distribution. Returns the probability that X > x, equivalent to the survival function. | NULL | [dist_weibull_cdf_complement(1.5, 1.0, 0.5)] |
| dist_weibull_chf | scalar | Computes the cumulative hazard function of the weibull distribution. | NULL | [dist_weibull_chf(1.5, 1.0, 0.5)] |
| dist_weibull_hazard | scalar | Computes the hazard function of the weibull distribution. | NULL | [dist_weibull_hazard(1.5, 1.0, 0.5)] |
| dist_weibull_kurtosis | scalar | Returns the kurtosis of the weibull distribution. | NULL | [dist_weibull_kurtosis(1.5, 1.0)] |
| dist_weibull_kurtosis_excess | scalar | Returns the excess kurtosis of the weibull distribution. | NULL | [dist_weibull_kurtosis_excess(1.5, 1.0)] |
| dist_weibull_log_cdf | scalar | Computes the natural logarithm of the cumulative distribution function (CDF) of the weibull distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x. | NULL | [dist_weibull_log_cdf(1.5, 1.0, 0.5)] |
| dist_weibull_log_cdf_complement | scalar | Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the weibull distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function. | NULL | [dist_weibull_log_cdf_complement(1.5, 1.0, 0.5)] |
| dist_weibull_log_pdf | scalar | Computes the natural logarithm of the probability density function (log-PDF) of the weibull distribution. Useful for numerical stability when dealing with very small probabilities. | NULL | [dist_weibull_log_pdf(1.5, 1.0, 0.5)] |
| dist_weibull_median | scalar | Returns the median (50th percentile) of the weibull distribution, which equals the mean. | NULL | [dist_weibull_median(1.5, 1.0)] |
| dist_weibull_mode | scalar | Returns the mode (most likely value) of the weibull distribution, which equals the mean. | NULL | [dist_weibull_mode(1.5, 1.0)] |
| dist_weibull_pdf | scalar | Computes the probability density function (PDF) of the weibull distribution. Returns the probability densityat point x for a weibull distribution with specified parameters. | NULL | [dist_weibull_pdf(1.5, 1.0, 0.5)] |
| dist_weibull_quantile | scalar | Computes the quantile function (inverse CDF) of the weibull distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability. | NULL | [dist_weibull_quantile(1.5, 1.0, 0.95)] |
| dist_weibull_quantile_complement | scalar | Computes the complementary quantile function of the weibull distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles. | NULL | [dist_weibull_quantile_complement(1.5, 1.0, 0.05)] |
| dist_weibull_range | scalar | Returns the range of the weibull distribution. | NULL | [dist_weibull_range(1.5, 1.0)] |
| dist_weibull_sample | scalar | Generates random samples from the weibull distribution with specified parameters. | NULL | [dist_weibull_sample(1.5, 1.0)] |
| dist_weibull_skewness | scalar | Returns the skewness of the weibull distribution. | NULL | [dist_weibull_skewness(1.5, 1.0)] |
| dist_weibull_support | scalar | Returns the support of the weibull distribution. | NULL | [dist_weibull_support(1.5, 1.0)] |
| dist_weibull_variance | scalar | Returns the variance (σ²) of the weibull distribution. | NULL | [dist_weibull_variance(1.5, 1.0)] |
Overloaded Functions
This extension does not add any function overloads.
Added Types
This extension does not add any types.
Added Settings
This extension does not add any settings.