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

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

If the number of allowable x-values is not very large, the relative frequency of data at each x-value can be used directly as parameters in a Discrete distribution. Excel's FREQUENCY or ModelRisk's VoseFrequency functions are ideal for this purpose. The obvious difficulty with using the frequency of observations is that there will be gaps where no observations have been observed, and the variable may extend beyond the observed range.

If the number of allowable x-values is very large, it is easier to arrange the data into histogram form and then define a Cumulative distribution, as shown for a continuous variable. The discrete nature of the variable can be reintroduced by embedding the Cumulative distribution inside the standard spreadsheet ROUND(...) function. There is an advantage to using this method when there are gaps in your observations because they will automatically be smoothed.

 

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