What is Uniform Distribution?

In statistics, a type of聽probability distribution聽in which all outcomes are equally likely. 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 y-axis at 0.50.

Understanding 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.

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 point in the continuous range between 0.0 and 1.0 has an equal opportunity of appearing, yet there are an infinite number of points between 0.0 and 1.0.

There are several other important continuous distributions, such as the normal distribution, chi-square, and Student's t-distribution.

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聽and moment generating functions.

Key Takeaways

  • Uniform distributions are probability distributions with equally likely outcomes.
  • There are two types of uniform distributions: discrete and continuous. In the former type of distribution, each outcome is discrete. In a continuous distribution, outcomes are continuous and infinite.

Visualizing 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 values of a聽random variable 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.聽

Under a uniform distribution, each value in the set of possible values has 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鈥攖hat is, 1/4.