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:



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:


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.


Discrete Uniform distribution equations