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Uniform Distribution

The Uniform distribution is a continuous distribution bounded on both sides. Its density does not depend on the value of x. It is a special case of the Beta distribution. It is frequently called rectangular distribution. Most random number generators provide samples from the Uniform distribution on (0,1) and then convert these samples to random variates from other distributions.

The Uniform distribution is used to represent a random variable with constant likelihood of being in any small interval between min and max. Note that the probability of either the min or max value is 0; the endpoints do NOT occur.

f(x) = 1 / max – min

min = minimum x
max = maximum x

When use a Uniform Distribution

The uniform distribution is usually used when you want your results to range between two numbers.


ProcessModel uses the following formula for uniform distribution in its simulation engine:

U(<mean>,<half range>)


You have a time range of 10-15 minutes and you want the ProcessModel simulation engine to choose a time within that time range, the formula for uniform distribution to use over here will be:


Mean: (10 + 15) / 2 = 12.5

Half Range (the maximum up or down a value can go from mean): (Up: 12.5 + 2.5 = 15 — Down: 12.5 – 2.5 = 10) = 2.5

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About the Author:

Scott Baird has been president of ProcessModel for more than 15 years. His focus has been to teach others how to improve processes dramatically. He has been successful in transferring these skills to over 200 companies, including ESPN, NASA, GE, Nationwide, Cendant, SSA and many more. Specialties: Group facilitation for process improvement, process design and simulation, simulation modeling, business management and training others to see opportunities. Scott loves to teach process improvement and has often been heard to say, “Of all the things I do, training others to improve processes is my favorite.” Scott is a father of four and a grandfather of eight. He is an avid woodworker, designing and creating presentation boxes. In his spare time, he volunteers in a college preparation program.