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

Bar-Lev, Shaul K.; Batsidis, Apostolos; Einbeck, Jochen; Liu, Xu; Ren, Panpan

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


Authors

Shaul K. Bar-Lev

Apostolos Batsidis

Xu Liu

Panpan Ren



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.

Citation

Bar-Lev, S. K., Batsidis, A., Einbeck, J., Liu, X., & Ren, P. (2023). Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions. Mathematics, 11(7), Article 1603. https://doi.org/10.3390/math11071603

Journal Article Type Article
Acceptance Date Mar 22, 2023
Online Publication Date Mar 26, 2023
Publication Date Apr 1, 2023
Deposit Date May 5, 2023
Publicly Available Date May 5, 2023
Journal Mathematics
Electronic ISSN 2227-7390
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 11
Issue 7
Article Number 1603
DOI https://doi.org/10.3390/math11071603
Related Public URLs https://econpapers.repec.org/article/gamjmathe/v_3a11_3ay_3a2023_3ai_3a7_3ap_3a1603-_3ad_3a1107781.htm

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