Probability Distribution Functions and Inverses

Functions

Discrete Random Variables: Distribution Functions and Probability Functions

Distribution Functions

Binomial distribution function binomial_cdf

Binomial probability function binomial_pdf

Discrete geometric cumulative distribution function geometric_cdf

Inverse of the discrete geometric cumulative
distribution function geometric_inverse_cdf

Discrete geometric probability density function geometric_pdf

Hypergeometric distribution function hypergeometric_cdf

Hypergeometric probability function hypergeometric_pdf

Poisson distribution function poisson_cdf

Poisson probability function poisson_pdf

Discrete uniform cumulative distribution function discrete_uniform_cdf

Inverse of the discrete uniform cumulative
distribution function discrete_uniform_inverse_cdf

Discrete uniform probability density function discrete_uniform_pdf

Continuous Random Variables

Distribution Functions and their Inverses

Beta distribution function beta_cdf

Inverse beta distribution function beta_inverse_cdf

Noncentral beta cumulative distribution
function (CDF) non_central_beta_cdf

Inverse of the noncentral beta CDF non_central_beta_inverse_cdf

Noncentral beta probability density function (PDF) non_central_beta_pdf

Bivariate normal distribution function bivariate_normal_cdf

Chi-squared distribution function chi_squared_cdf

Inverse chi-squared distribution function chi_squared_inverse_cdf

Calculates the complement of the chi-squared
distribution complementary_chi_squared_cdf

Noncentral chi-squared distribution function non_central_chi_sq

Inverse of the noncentral chi-squared distribution function non_central_chi_sq_inv

Noncentral chi-squared probability
density function (PDF) non_central_chi_sq_pdf

Exponential cumulative distribution function exponential_cdf

Inverse of the exponential cumulative
distribution function exponential_inverse_cdf

Exponential probability density function exponential_pdf

F distribution function F_cdf

Inverse F distribution function F_inverse_cdf

Calculates the complement of the F distribution
function complementary_F_cdf

Noncentral F probability density
function (PDF) non_central_F_pdf

Noncentral F cumulative distribution
function (CDF) non_central_F_cdf

Calculates the complement of the noncentral
F CDF complementary_non_central_F_cdf

Inverse of the noncentral F distribution function non_central_F_inverse_cdf

Gamma distribution function gamma_cdf

Inverse gamma distribution function gamma_inverse_cdf

Generalized Gaussian cumulative distribution function generalized_gaussian_cdf

Inverse of the generalized Gaussian cumulative distribution function generalized_gaussian_inverse_cdf

Generalized Gaussian probability density function generalized_gaussian_pdf

Lognormal cumulative distribution function lognormal_cdf

Inverse of the lognormal cumulative distribution function lognormal_inverse_cdf

Lognormal probability density function lognormal_pdf

Normal (Gaussian) distribution function normal_cdf

Multivariate normal distribution function multivariate_normal_cdf

Inverse normal distribution function normal_inverse_cdf

Student’s t distribution function t_cdf

Inverse Student’s t distribution function t_inverse_cdf

Calculates the complement of the Student’s t
distribution complementary_t_cdf

Noncentral Student’s t distribution function non_central_t_cdf

Inverse of the noncentral Student’s t distribution function non_central_t_inv_cdf

Noncentral Student’s t probability density function non_central_t_pdf

Pareto cumulative probability distribution function pareto_cdf

Pareto probability density function pareto_pdf

Parameter Estimation

Maximum likelihood estimation for univariate
probability distributions max_likelihood_estimates