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.

## Formula

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

U(<mean>,<half range>)

Example:

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:

U(12.5,2.5)

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