# Statistical Distribution Functions

There are a variety of ways to describe probability distributions such as probability density or mass, cumulative versions of density and mass, inverses of the cumulative descriptions, or hazard functions. The distribution functions can be computed for all symbolic distributions whether parametric, nonparametric, derived, or formula distribution. Distribution functions can be used to show that two distributions are equal in distribution or compare goodness of fit to data using hypothesis tests, or using quantile plots or plots against histograms for the corresponding distributions. A closely related concept is that of the likelihood function, which is used to describe goodness of fit for a distribution parameter estimation. A similarly closely related concept is that of the generating function, which is a transformed version of the probability density function.

PDF probability density and probability mass function

CDF cumulative distribution function

SurvivalFunction survival or reliability function

HazardFunction hazard function or failure rate

RarerProbability probability for a rarer event

### Inverse Distribution Functions

InverseCDF, Quantile inverse CDF or quantile function

InverseSurvivalFunction inverse survival function

### Likelihood Functions

Likelihood likelihood function

LogLikelihood log-likelihood function

### Distribution Properties

DistributionParameterAssumptions assumptions on distribution parameters

DistributionParameterQ test if a distribution has valid parameters