# Discrete Uniform

1. The Discrete Uniform distribution can be constructed with Crystal Ball's Custom distribution.

2. In the special case when we model all integer values between a certain minimum and maximum, we can use Crystal Ball's Integer Uniform Distribution (min, max)

Discrete uniform equations

Crystal Ball parameter restrictions

The Discrete Uniform distribution is a special case of the Discrete distribution. It describes a variable that can take one of several explicit discrete values with equal probabilities of taking any particular value.

An example of the Discrete Uniform distribution that has to be constructed with Crystal Ball's Custom distribution, is shown below. When we model all integer values between a specified minimum and maximum, we can use the Integer Uniform distribution. An example of the Integer Uniform distribution in Crystal Ball is shown below, and the Integer Uniform distribution in Crystal Ball is used in Cell I9 of the sheet "Joint" of the model Empirical_distributions. #### Uses

It is not often that we come across a variable that can take one of several values each with equal probability. However, there are a couple of modeling techniques that require that capability:

##### - Bootstrap

Resampling in univariate non-parametric Bootstrap (although the Integer Uniform distribution is more commonly used)

##### - Fitting empirical distribution to data

Creating an empirical distribution directly from a data set, i.e. where we believe that the list of data values is a good representation of the randomness of the variable, as is illustrated here.

The algorithm for generating values from the Discrete Uniform distribution is slow because it is simply selecting values from a list. You should therefore try to avoid having large arrays of this function in your model.

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