# Uniform Distribution

## DEFINITION of 'Uniform Distribution'

In statistics, a type of probability distribution in which all outcomes are equally likely. A deck of cards has a uniform distribution because the likelihood of drawing a heart, a club, a diamond or a spade is equally likely. A coin also has a uniform distribution because the probability of getting either heads or tails in a coin toss is the same.

## BREAKING DOWN 'Uniform Distribution'

There are two types of uniform distributions: discrete and continuous. The possible results of rolling a die provide an example of a discrete uniform distribution: it is possible to roll a 1, 2, 3, 4, 5 or 6, but it is not possible to roll a 2.3, 4.7 or 5.5.

Uniform distribution is a statistical probability definition whereby every variable has the same probable outcome. Distributions are simple ways to help statisticians, mathematicians and investors to organize, analyze and display variable probabilities.

## Understanding Uniform Distributions

A distribution is a simple way to appear in a set of data, either in a graph or in a list of stating which random variables have lower or higher chances, or probability. There are many different types of probability distributions, yet uniform distributions are the simplest of them all. Many people understand the bell curve distribution, as it is often used in college grading systems. Usually, students in a class organically fall into a bell curve distribution, with most students achieving an average mark, with a few at either end achieving a very poor or a very good grade.

However, a uniform distribution is a set of variables that all have the exact same possibility of happening. This uniform distribution, when displayed as a bar graph, has the exact same height of each bar and a standard number of bars. In this way, it typically looks like a rectangle and therefore is often described as the rectangle distribution. If you think about the possibility of pulling each suit's face card from a deck of playing cards, there is a random yet equal chance of pulling the jack of hearts as there is for pulling the king of spades.

## Continuous Uniform Distributions

The other type of uniform distributions is continuous. An idealized random number generator would be considered a continuous uniform distribution. With this type of distribution, every variable has an equal opportunity of appearing, yet there are a continuous or possibly infinite number of possibilities. There are four other important distributions among the infinite possible distributions: binomial distribution, chi-square, normal and Student's t distribution models.

## Functions of Distributions

There are also multiple functions associated with distributions to help consider variables and their variance within a data set. These functions include probability density function, cumulative density and moment generating functions.