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This research aims to develop goodness-of-fit tests for probabilistic models applicable to reliability data, focusing on asymmetric shapes.

Goodness-of-fit tests based on Mellin statistics for reliability data

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Randomized trial evaluates goodness-of-fit tests for reliability data, suggesting effective model validation methods.

This research aims to develop goodness-of-fit tests for probabilistic models applicable to reliability data, focusing on asymmetric shapes.
Three tests based on adaptations of Hotelling’s T2 statistic targeting different aspects of log-cumulants are introduced.
The methodology includes deriving the correct asymptotic null distribution and implementing parametric bootstrap p-values for finite-sample inference.
Tests are evaluated using simulation studies and applied to nine real reliability datasets.
The tests demonstrate good size control and competitive power against existing shape-based alternatives.
They provide complementary insights compared to Anderson-Darling and Cramér-von Mises tests.
Effective differentiation between log-normal and log-logistic distributions is achieved.

Santos et al. (2026) studied this question.

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