Discrete Uniform distribution | Vose Software

# Discrete Uniform distribution

Format: DUniform({x})

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 is shown below:

## 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 Monte Carlo simulation modeling techniques that require that capability:

### Bootstrap

Resampling in univariate non-parametric Bootstrap.

### 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.

The algorithm for generating random values from the DUniform is relatively slow because it is simply selecting values from a list. You should therefore avoid having large arrays of this function in your model if possible.

## ModelRisk functions added to Microsoft Excel for the Discrete Uniform distribution

VoseDUniform generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseDUniformObject constructs a distribution object for this distribution.

VoseDUniformProb returns the probability mass or cumulative distribution function for this distribution.

VoseDUniformProb10 returns the log10 of the probability mass or cumulative distribution function.