# Histogram distribution

Format: Histogram(min, max, {fi})

The Histogram distribution takes three parameters: a minimum; a maximum; and a list (array) of frequencies (or relative frequencies) for a number of equally spaced bands between the minimum and maximum.

The figure below plots an example.

Histogram(2,9,{1,2,4,6,3,2,1})

## Uses

The distribution is useful in a non-parametric technique for replicating the distribution shape of a large set of data. The technique is simply to collate the data into a number of equal bands between a minimum and maximum you determine, calculate the number of data values that fall into each band, and then use this information to define the distribution. It has the disadvantage of 'squaring off' into the histogram shape, but with a lot of data and small bands the technique is a transparent and practical way of fitting a distribution to data.

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

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

VoseHistogramObject constructs a distribution object for this distribution.

VoseHistogramProb returns the probability density or cumulative distribution function for this distribution.

VoseHistogramProb10 returns the log10 of the probability density or cumulative distribution function.

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

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

VoseHistogramFitP returns the parameters of this distribution fitted to data.