Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions

The class of natural exponential families (NEFs) distributions having power variance functions (NEF-PVFs) is huge (uncountable), with enormous applications in various fields. Based on a characterization property that holds for the cumulants members this class, we developed novel goodness-of-fit (gof) test testing whether given random sample fits fixed class. We derived asymptotic null distribution statistic and an appropriate bootstrap scheme. As content paper mainly theoretical, exemplify its applicability to only few elements NEF-PVF specifically, gamma modified Bessel-type NEFs. A Monte Carlo study was executed examining performance both—the counterpart—in controlling type I error rate evaluating their special case gamma, while real data examples demonstrate gof Bessel distribution.