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**P-Values and Distribution Fitting**

**Applies to:** @RISK 5.x–7.x

Why doesn't @RISK give p-values for the Kolmogorov-Smirnov and Anderson-Darling tests for most fits? Why do the ones that @RISK does give disagree with other software packages?

Basically, the p-values require knowledge of the sampling distribution of the K-S or A-D statistic. In general this sampling distribution is not known exactly, though there are some very particular circumstances where it is.

While we don't know the exact methodology that other packages use, it is true that there are a number of ways to deal with this problem. The method @RISK takes is very cautious. If we cannot report the p-value, either we report a possible range of values it could be (if we can determine that) or we don't return a value at all. Some people will choose the "no-parameters-estimated case", which can be determined in many cases, but which returns an ultra-conservative answer. A good reference for how @RISK handles this can be found in the book *Goodness-of-Fit Techniques* by D'Agostino and Stephens.

Sometimes too much stress is laid on p-values in distribution fitting. It's really not valid to select a p-value as a "bright-line test" and say that any fit with a higher p-value is good and any fit with a lower p-value is bad. There is no substitute for looking at the fitted distribution overlaid on the data.

We recommend against using the p-values for your primary determination of which distribution is the best one for your data set. For some guidance, see "Fit Statistics" in the @RISK help file or in Appendix A of the user manual, and Interpreting AIC Statistics in this Knowledge Base.

Last edited: 2015-06-19

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