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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

License:

Apache-2.0

Authors:

John Michael Hall, Ilya Yaroshenko

public import mir.stat.distribution.bernoulli;
public import mir.stat.distribution.beta;
public import mir.stat.distribution.beta_proportion;
public import mir.stat.distribution.binomial;
public import mir.stat.distribution.cauchy;
public import mir.stat.distribution.chi2;
public import mir.stat.distribution.cornish_fisher;
public import mir.stat.distribution.exponential;
public import mir.stat.distribution.f;
public import mir.stat.distribution.gamma;
public import mir.stat.distribution.generalized_pareto;
public import mir.stat.distribution.geometric;
public import mir.stat.distribution.gev;
public import mir.stat.distribution.hypergeometric;
public import mir.stat.distribution.laplace;
public import mir.stat.distribution.log_normal;
public import mir.stat.distribution.logistic;
public import mir.stat.distribution.negative_binomial;
public import mir.stat.distribution.normal;
public import mir.stat.distribution.pareto;
public import mir.stat.distribution.poisson;
public import mir.stat.distribution.rayleigh;
public import mir.stat.distribution.students_t;
public import mir.stat.distribution.uniform;
public import mir.stat.distribution.uniform_discrete;
public import mir.stat.distribution.weibull;

Library Reference

mir.stat.distribution