Applies to: @RISK 5.x and Up

 

Getting p-values, critical values, and confidence intervals for fitted distributions

Problem
You want to obtain p-values, critical values, or confidence intervals for parameters when fitting a distribution to data in @RISK.

 

Solution – Parametric Bootstrap

1. Open the Fit Distributions to Data dialog.

2. On the Bootstrap tab, tick Run Parametric Bootstrap.

3. Specify the number of resamples and the confidence level for the parameters. Note that bootstrapping may take additional time, especially for large data sets.

4. Click Fit as usual. A pop-up window will track the bootstrap progress.

5. After fitting finishes:

   • Click the Statistical Summary icon (last small icon at the bottom) for an exhaustive chart of all distributions.

   • Or, select a single distribution and click the Bootstrap Analysis icon (second from right) to see fit statistics, p-values, or parameter confidence intervals for that distribution.

If the bootstrapping fails, a message will appear: “Unable to refit one or more bootstrap resamples.”

 

Why p-values for K-S and A-D tests are limited
Kolmogorov-Smirnov (K-S) and Anderson-Darling (A-D) p-values require the sampling distribution of the test statistic, which is generally unknown except in special cases. Different software packages may use different approximations. @RISK takes a cautious approach: it reports a possible range of values or does not return a value if the sampling distribution is uncertain. Some approaches, like the “no-parameters-estimated case,” are ultra-conservative. For more details, see Goodness-of-Fit Techniques by D’Agostino and Stephens.

 

Cautions for using p-values
P-values should not be the sole criterion for selecting the best-fitting distribution. High or low p-values alone do not guarantee a good or bad fit. Always visually inspect the fitted distribution overlaid on the data, as this provides more reliable insight than relying solely on p-values.

 

 

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