Fitting a distribution for a discrete variable

This section discusses techniques for fitting a distribution to observations for a discrete variable.

Before proceeding we suggest that you review the section on checking for data quality and discrete data transformation first.

The methods we describe can be categorised into four two groups: non-parametric and parametric distribution fit, depending on your choice of a parametric or non-parametric distribution, and of a first or second order distribution:.

Fitting a discrete non-parametric first-order distribution to data

Fitting a discrete non-parametric second-order distribution to data

Fitting a discrete parametric first-order distribution to data

Fitting a discrete parametric second-order distribution to data

Using a continuous distribution to approximate a discrete variable

It is sometimes more convenient to use a continuous distribution to model a discrete variable, usually when using a wide ranging non-parametric distribution because the variable takes many possible values and the discrete version becomes difficult to handle. Continuous parametric distributions also offer a wider range of shapes than the range of discrete parametric distributions, so you may well get a better representation of your observed pattern. Excel's ROUND(Distribution,0) function can be used to get the continuous distribution to return discrete values:

Fitting a continuous non-parametric first-order distribution to data

Fitting a continuous non-parametric second-order distribution to data

Fitting a continuous parametric first-order distribution to data

Fitting a continuous parametric second-order distribution to data

Fitting a distribution for a discrete variable

Using a continuous distribution to approximate a discrete variable

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