Goodness-of-fit Measures Based on the Mellin Transform for Beta
Generalized Lifetime Data
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.