# Discrete distribution

Format: Discrete({x}, {p})

The Discrete distribution is a general type of probability distribution used to describe a variable that can take one of several explicit discrete values {x} and where a probability weights {p} are assigned to each value. For example, the number of bridges to be built over a motorway extension or the number of times a software module will have to be re-coded after testing. An example of the Discrete distribution is shown below:

## Other uses

A Discrete distribution is also particularly useful to describe probabilistic branching. For example, a firm estimates that it will sell Normal(120,10) tonnes of weed killer next year unless a rival firm comes out with a competing product, in which case it estimates it sales will drop to Normal(85,9) tonnes. It also estimates that there is a 30% chance of the competing product appearing. This could be modelled by:

Sales = Discrete(A1:A2,B1:B2) where the cells A1:B2 contain the formulae:

A1: =Normal (120, 10)

A2: =Normal (85, 9)

B1: 70%

B2: 30%

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

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

VoseDiscreteObject constructs a distribution object for this distribution.

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

VoseDiscreteProb10 returns the log10 of the probability mass or cumulative distribution function.

VoseDiscreteFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseDiscreteFitObject constructs a distribution object of this distribution fitted to data.

VoseDiscreteFitP returns the parameters of this distribution fitted to data.