Using Goodness-of Fit Statistics to optimize Distribution Fitting | Vose Software

Using Goodness-of Fit Statistics to optimize Distribution Fitting

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

Goodness of fit statistics can be used with a linear optimiser to find the parameters that produce the closest fit of a distribution to the observed data. The technique proceeds as follows:

1.     The MLE of the fitted distribution (or any reasonable guess for the best fit parameter) is determined.

2.     A spreadsheet is written that calculates the relevant goodness-of-fit statistic with the MLE displayed in a separate cell

3.     Using the Solver in Excel, the value of the parameter is varied to produce a minimum value for the goodness-of-fit statistic. The parameter value  that produces that minimum is then used instead of the original estimator.

In fact for normal statistical applications, the MLE is a far better estimate than a parameter value that minimises a goodness-of-fit statistic. However, this technique does offer the advantage of allowing the analyst to select or develop his/her own measure of goodness-of-fit and then to find the parameters that optimise that measure.

All fitting functions in ModelRisk use MLE methods for fitting.

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