DEFINITION of 'Uniform Distribution'
In statistics, a type of probability distribution in which all outcomes are equally likely; each variable has the same probability that it will be the outcome. A deck of cards has within it uniform distributions 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.
The uniform distribution can be visualized as a straight horizontal line, so for a coin flip returning a head or tail, both have a probability p = 0.50 and would be depicted by a line from the yaxis at 0.50.
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. Therefore, the roll of a die generates a discrete distribution with p = 1/6 for each outcome. A uniform distribution with only two possible outcomes is a special case of the binomial distribution.
Understanding Uniform Distributions
A distribution is a simple way to visualize a set of data, either as a graph or in a list of stating which random variables have lower or higher chances of happening. There are many different types of probability distributions, and the uniform distribution is perhaps the simplest of them all.
Under a uniform distribution, the set of variables all have the exact same possibility of happening. This distribution, when displayed as a bar or line graph, has the same height for each potential outcome. In this way, it can look like a rectangle and therefore is sometimes described as the rectangle distribution. If you think about the possibility of drawing a particular suit from a deck of playing cards, there is a random yet equal chance of pulling a hearts as there is for pulling a spade  that is, 1/4.
Continuous Uniform Distributions
Some uniform distributions are continuous rather than discrete. 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 points that can exist.
There are several other important continuous distributions, such as the normal distribution, chisquare, and Student's tdistribution.
Functions of Distributions
There are also several data generating or data analyzing functions associated with distributions to help understand the variables and their variance within a data set. These functions include probability density function, cumulative density and moment generating functions.

Probability Distribution
A probability distribution is a statistical function that describes ... 
Discrete Distribution
A discrete distribution is a function that gives the probabilities ... 
Normal Distribution
The normal distribution is a continuous probability distribution ... 
Distribution
Distribution occurs when a mutual fund, company or retirement ... 
Random Variable
A random variable is a variable whose value is unknown or a function ... 
Distribution Network
A distribution network is a company's interconnected group of ...

Financial Advisor
Series 66 Exam Prep: The Uniform Securities Act
Before you take the series 66, you need to understand the Uniform Securities Act and the Blue Sky Laws. 
Financial Advisor
Stretch Your Savings By Working Into Your 70s
Staying employed a little longer may allow for a more comfortable retirement. 
Financial Advisor
How to Save Clients from RMD Aggregation Mistakes
Advisors can help clients avoid required minimum distribution mistakes in their retirement plans. 
Investing
Optimize your portfolio using normal distribution
Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk. 
Financial Advisor
Tough Times: Should You Dip Into Your Qualified Plan?
401(k)s, pensions and profitsharing plans can be a source of cash, but there are consequences to this option. 
Retirement
How a 401(k) Works After Retirement
Find out how your 401(k) works after you retire, including when you are required to begin taking distributions and the tax impact of your withdrawals.