Simulation – Stat::Fit

1. Simulation – Stat::Fit

2. Stat::Fit • A utility package within the ProModel software used for analyzing user-input data and fitting an appropriate empirical distribution to it • Explanation of some of the statistical tools used (i.e. goodness of fit tests) is beyond the scope of this course • Relative rank is determined by an empirical method which uses effective goodness of fit calculations • Acceptance of fit usually reflects the results of the goodness of fit tests at a particular level of significance • level of significance is the probability of incorrectly rejecting the hypothesis that the selected distribution with estimated parameters fits the input data • level of significance is assumed to be set to 0.05

3. Goodness of fit tests • Goodness of fit tests are merely comparisons of the input data to the fitted distributions in a statistically significant manner • Each test makes the hypothesis that the fit is good and calculates a test statistic for comparison to a standard • Goodness of fit tests include: • Chi Squared test • Kolmogorov Smirnov test • Anderson Darling test • If the choice of test is uncertain, even after consulting the descriptions, use the Kolmogorov Smirnov test which is applicable over the widest range of data and fitted parameters

4. P-value • While the test statistic for each test can be useful, the p-value for each test is more useful in determining the goodness of fit • The p-value is defined as the probability that another sample will be as unusual as the current sample given that the fit is appropriate • A small p-value indicates that the current sample is highly unlikely, and, therefore, the fit should be rejected • Conversely, a high p-value indicates that the sample is likely and would be repeated, and, therefore, the fit should not be rejected • The HIGHER the p-value, the more likely that the fit is appropriate • When comparing two different fitted distributions, the distribution with the higher p-value is likely to be the better fit regardless of the level of significance

5. Distribution in ProModel Format • Click on the “export” button and make sure “ProModel Products” is selected as the “Application” in the popup window • Select the appropriate “Fitted Distribution” and the format needed for ProModel will be displayed