mir.stat.distribution

This package publicly imports mir.stat.distribution.* modules.

import mir.math.common: pow;
import mir.stat.distribution;
import mir.test: shouldApprox;

4.binomialPMF(6, 2.0 / 3).shouldApprox == (15.0 * pow(2.0 / 3, 4) * pow(1.0 / 3, 2));

Each individual distribution module contains - where feasible - functions for: - Probability density/mass functions (e.g. mir.stat.distribution.*PDF/mir.stat.distribution.*PMF) - Cumulative distriution functions (e.g. mir.stat.distribution.*CDF) - Complementary cumulative distribution functions (e.g. mir.stat.distribution.*CCDF) - Inverse cumulative distribution functions (e.g. mir.stat.distribution.*InvCDF) - Log probaiity density/mass functions (e.g. mir.stat.distribution.*LPDF/mir.stat.distribution.*LPMF)

In addition, convenience modules are provided (mir.stat.distribution.pdf, mir.stat.distribution.cdf, mir.stat.distribution.invcdf) that publicly import only the respective functions from each individual distribution module (note: the pdf module also contains pmfs).

Some (discrete) distributions include multiple algorithms for calculating the included functions. The default is a direct calculation with others being approximations. As a convention, these modules leave it to the user to determine when to switch between the different approximations. Care should be taken if more extreme parameters are used as it can have an impact on speed.


Modules	Description
Convenience Modules (with public imports)
mir.stat.distribution	Statistical Distributions
mir.stat.distribution.pdf	Probability Density/Mass Functions
mir.stat.distribution.cdf	Cumulative Distribution Functions
mir.stat.distribution.invcdf	Inverse Cumulative Distribution Functions
Univariate Discrete Distributions
mir.stat.distribution.bernoulli	Bernoulli Distribution
mir.stat.distribution.binomial	Binomial Distribution
mir.stat.distribution.geometric	Geometric Distribution
mir.stat.distribution.hypergeometric	Hypergeometric Distribution
mir.stat.distribution.negative_binomial	Negative Binomial Distribution
mir.stat.distribution.poisson	Poisson Distribution
mir.stat.distribution.uniform_discrete	Discrete Uniform Distribution
Univariate Continuous Distributions
mir.stat.distribution.beta	Beta Distribution
mir.stat.distribution.beta_proportion	Beta Proportion Distribution
mir.stat.distribution.cauchy	Cauchy Distribution
mir.stat.distribution.chi2	Chi-squared Distribution
mir.stat.distribution.cornish_fisher	Cornish-Fisher Expansion
mir.stat.distribution.exponential	Exponential Distribution
mir.stat.distribution.f	F Distribution
mir.stat.distribution.gamma	Gamma Distribution
mir.stat.distribution.generalized_pareto	Generalized Pareto Distribution
mir.stat.distribution.gev	Generalized Extreme Value (GEV) Distribution
mir.stat.distribution.laplace	Laplace Distribution
mir.stat.distribution.log_normal	Log-normal Distribution
mir.stat.distribution.logistic	Logistic Distribution
mir.stat.distribution.normal	Normal Distribution
mir.stat.distribution.pareto	Pareto Distribution
mir.stat.distribution.rayleigh	Rayleigh Distribution
mir.stat.distribution.students_t	Student's t Distribution
mir.stat.distribution.uniform	Continuous Uniform Distribution
mir.stat.distribution.weibull	Weibull Distribution
Multivariate Distributions
mir.stat.distribution.categorical	Categorical Distribution

Modules

bernoulli module mir.stat.distribution.bernoulli: This module contains algorithms for the Bernoulli Distribution.
beta module mir.stat.distribution.beta: This module contains algorithms for the Beta Distribution.
beta_proportion module mir.stat.distribution.beta_proportion: This module contains algorithms for the Beta Proportion Distribution.
binomial module mir.stat.distribution.binomial: This module contains algorithms for the Binomial Distribution.
categorical module mir.stat.distribution.categorical: This module contains algorithms for the Categorical Distribution.
cauchy module mir.stat.distribution.cauchy: This module contains algorithms for the Cauchy Distribution.
cdf module mir.stat.distribution.cdf: This package publicly imports mir.stat.distribution.*CDF modules.
chi2 module mir.stat.distribution.chi2: This module contains algorithms for the Chi-squared Distribution.
cornish_fisher module mir.stat.distribution.cornish_fisher: This module contains algorithms for the Cornish-Fisher Expansion.
exponential module mir.stat.distribution.exponential: This module contains algorithms for the Exponential Distribution.
f module mir.stat.distribution.f: This module contains algorithms for the F Distribution.
gamma module mir.stat.distribution.gamma: This module contains algorithms for the Gamma Distribution.
generalized_pareto module mir.stat.distribution.generalized_pareto: This module contains algorithms for the Generalized Pareto Distribution.
geometric module mir.stat.distribution.geometric: This module contains algorithms for the Geometric Distribution.
gev module mir.stat.distribution.gev: This module contains algorithms for the Generalized Extreme Value (GEV) Distribution.
hypergeometric module mir.stat.distribution.hypergeometric: This module contains algorithms for the Hypergeometric Distribution.
invcdf module mir.stat.distribution.invcdf: This package publicly imports mir.stat.distribution.*InvCDF modules.
laplace module mir.stat.distribution.laplace: This module contains algorithms for the Laplace Distribution.
log_normal module mir.stat.distribution.log_normal: This module contains algorithms for the Log-normal Distribution.
logistic module mir.stat.distribution.logistic: This module contains algorithms for the Logistic Distribution.
negative_binomial module mir.stat.distribution.negative_binomial: This module contains algorithms for the Negative Binomial Distribution.
normal module mir.stat.distribution.normal: This module contains algorithms for the Normal Distribution.
pareto module mir.stat.distribution.pareto: This module contains algorithms for the Pareto Distribution.
pdf module mir.stat.distribution.pdf: This package publicly imports mir.stat.distribution.*PDF & .*PMF modules.
poisson module mir.stat.distribution.poisson: This module contains algorithms for the Poisson Distribution.
rayleigh module mir.stat.distribution.rayleigh: This module contains algorithms for the Rayleigh Distribution.
students_t module mir.stat.distribution.students_t: This module contains algorithms for the Student's t Distribution.
uniform module mir.stat.distribution.uniform: This module contains algorithms for the continuous Uniform Distribution.
uniform_discrete module mir.stat.distribution.uniform_discrete: This module contains algorithms for the Discrete Uniform Distribution.
weibull module mir.stat.distribution.weibull: This module contains algorithms for the Weibull Distribution.

Public Imports

mir.stat.distribution.bernoulli public import mir.stat.distribution.bernoulli;

mir.stat.distribution.beta public import mir.stat.distribution.beta;

mir.stat.distribution.beta_proportion public import mir.stat.distribution.beta_proportion;

mir.stat.distribution.binomial public import mir.stat.distribution.binomial;

mir.stat.distribution.cauchy public import mir.stat.distribution.cauchy;

mir.stat.distribution.chi2 public import mir.stat.distribution.chi2;

mir.stat.distribution.cornish_fisher public import mir.stat.distribution.cornish_fisher;

mir.stat.distribution.exponential public import mir.stat.distribution.exponential;

mir.stat.distribution.f public import mir.stat.distribution.f;

mir.stat.distribution.gamma public import mir.stat.distribution.gamma;

mir.stat.distribution.generalized_pareto public import mir.stat.distribution.generalized_pareto;

mir.stat.distribution.geometric public import mir.stat.distribution.geometric;

mir.stat.distribution.gev public import mir.stat.distribution.gev;

mir.stat.distribution.hypergeometric public import mir.stat.distribution.hypergeometric;

mir.stat.distribution.laplace public import mir.stat.distribution.laplace;

mir.stat.distribution.log_normal public import mir.stat.distribution.log_normal;

mir.stat.distribution.logistic public import mir.stat.distribution.logistic;

mir.stat.distribution.negative_binomial public import mir.stat.distribution.negative_binomial;

mir.stat.distribution.normal public import mir.stat.distribution.normal;

mir.stat.distribution.pareto public import mir.stat.distribution.pareto;

mir.stat.distribution.poisson public import mir.stat.distribution.poisson;

mir.stat.distribution.rayleigh public import mir.stat.distribution.rayleigh;

mir.stat.distribution.students_t public import mir.stat.distribution.students_t;

mir.stat.distribution.uniform public import mir.stat.distribution.uniform;

mir.stat.distribution.uniform_discrete public import mir.stat.distribution.uniform_discrete;

mir.stat.distribution.weibull public import mir.stat.distribution.weibull;

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