Discrete Random Variables: Distribution Functions and Probability Functions

Distribution Functions

Binomial distribution function.......................................................................... binomial_cdf

Binomial probability function........................................................................... binomial_pdf

Hypergeometric distribution function..................................................... hypergeometric_cdf

Hypergeometric probability function...................................................... hypergeometric_pdf

Poisson distribution function........................................................................... poisson_cdf

Poisson probability function............................................................................ poisson_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

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

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 Students’s t distribution function ............................................ non_central_t_cdf

Inverse of the noncentral Student’s t
distribution function.......................................................................... non_central_t_inv_cdf

Noncentral Students’s t probability density
function (PDF)....................................................................................... non_central_t_pdf

Parameter Estimation

Maximum likelihood estimation for univariate
probability distributions.............................................................. max_likelihood_estimates

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