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.

See Also

 

ModelRisk

Monte Carlo simulation in Excel. Learn more

Tamara

Adding risk and uncertainty to your project schedule. Learn more

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