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

Shaul K. Bar-Lev, Apostolos Batsidis, Jochen Einbeck (), Xu Liu and Panpan Ren
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Shaul K. Bar-Lev: Faculty of Industrial Engineering and Technology Management, Holon Institute of Technology, Holon 6810201, Israel
Apostolos Batsidis: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Jochen Einbeck: Department of Mathematical Sciences and Research Methods Centre, Durham University, Durham DH13LE, UK
Xu Liu: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China
Panpan Ren: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China

Mathematics, 2023, vol. 11, issue 7, 1-20

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

Keywords: natural exponential family; goodness-of-fit tests; power variance function; Tweedie scale; Monte Carlo simulation; asymptotic distribution; bootstrap (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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