Goodness-of-fit Measures Based on the Mellin Transform for Beta Generalized Lifetime Data
• Josimar Vasconcelos,
• Renato Cintra,
• Abraão Nascimento
Josimar Vasconcelos
Federal Rural University of Pernambuco
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Renato Cintra
Federal University of Pernambuco
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Abraão Nascimento
Federal University of Pernambuco
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## Abstract

In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient goodness-of-fit (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fr\’{e}chet and Kumaraswamy distributions; and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fr\’{e}chet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling’s $T^2$ statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.

#### Peer review status:UNDER REVIEW

29 Mar 2021Submitted to Mathematical Methods in the Applied Sciences
30 Mar 2021Assigned to Editor
30 Mar 2021Submission Checks Completed
08 Apr 2021Reviewer(s) Assigned