Transforming discrete data before performing a parametric distribution fit

See also: Fitting distributions to data, Fitting in ModelRisk, Analyzing and using data

Discrete parametric distributions take integer values and generally start at zero. The variable you are modelling may not. For example, the number of people in a household, the number of animals in an outbreak, or the number of people involved in a car crash must be a minimum of one. In this situation, you should transform the data (e.g. by subtracting one) before fitting a distribution, and then add one back on afterwards (e.g. =1+VosePoisson(75)).

All parametric discrete distributions take integer values. However, your data may not because the variable may not be measured in the units that are integers. For example, you may have data on the amount of a compound (e.g. Paracetemol) that people have taken. The Paracetemol will have come in pills of specific doses (e.g. 25mg), so the observations will take 25mg steps. You would need to divide each data value by 25mg, fit a distribution to the resulting integer, and then multiply the resultant distribution by 25mg:

Original data are discrete but not with increments of 1

Data are transformed to integers

Transformed data are fit to a parametric distribution

Parametric distribution is transformed back to original scale

 

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