![]() The technical condition is whether the test statistic is asymptotically pivotal which means that the asymptotic distribution of the test statistic is independent of the specific parameters. The only solution to get p-values in those cases is either by bootstrap or by simulating the test statistic for the specific parameters. That is we would have to compute different distributions or tabulated p-values for each set of parameters, which is impossible. This is the case when parameters are not estimated and if the distribution is a simple location-scale family without shape parameters.įor distributions that have a shape parameter, the distribution of the test statistic that we need for computing the p-values depends on the parameters. In some cases we can tabulate or use a functional approximation to tabulated values. In both cases the distribution is not a standard distribution. ![]() P-values for Anderson-Darling or Kolmogorov-Smirnov depend on whether the parameters are estimated or not. We can use the Anderson-Darling, Kolmogorov-Smirnov or similar statistic just as distance measure to rank how well different distributions fit. I would just rank distributions by the goodness-of-fit statistic and not by p-values.
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