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A distribution is a mathematical description of probabilities or frequencies.

Overview

A distribution is a mathematical description of probabilities or frequencies. It can be applied to observed frequencies, estimated probabilities or frequencies, and theoretically hypothesized probabilities or frequencies. Distributions can be univariate, describing outcomes written with a single number, or multivariate, describing outcomes requiring ordered tuples of numbers.

Two devices are in common use to present univariate distributions. The cumulative form, or "cumulative distribution function" (CDF), gives--for every real number $x$--the chance (or frequency) of a value less than or equal to $x$. The "density" form, or "probability density function" (PDF), is the derivative (rate of change) of the CDF. The PDF might not exist (in this restricted sense), but a CDF always will exist. The CDF for a set of observations is called the "empirical density function" (EDF). Thus, its value at any number $x$ is the proportion of observations in the dataset less than or equal to $x$.

References

The following questions contain references to resources about probability distributions: