Simulation – Stat::Fit

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

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

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

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