Estimation and Goodness-of-fit for the q-Weibull Distribution via the Mellin Transform

Marília Oliveira (), Josimar Vasconcelos (), Frank Gomes-Silva () and Abraão Nascimento ()
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Marília Oliveira: Universidade Federal Rural de Pernambuco
Josimar Vasconcelos: Universidade Federal Rural de Pernambuco
Frank Gomes-Silva: Universidade Federal Rural de Pernambuco
Abraão Nascimento: Universidade Federal de Pernambuco

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 2, 1-21

Abstract: Abstract Recent technological advances have required processing a large amount of data and information from real phenomena. Understanding data behind an application is often made using flexible and interpretable probability distributions. In the survival analysis context, the q-distributions (particularly the q-Weibull) stand out for their efficiency in describing and explaining lifetime data. Despite the growing number of works dealing with new classes of distributions, there is a gap regarding the proposal of inference and goodness-of-fit methods. To achieve this, we first derive the Mellin transform for the q-Weibull law and propose both estimation and goodness-of-fit methods in terms of log-cumulants. The performance of our proposals is quantified from Monte Carlo experiments, on which the new estimators are compared with those due to moment methods and maximum likelihood. Finally, we apply our proposals to two real databases. Results suggest that using the proposed log-cumulants may yield meaningful improvements in the lifetime data analysis.

Keywords: q-Weibull model; Mellin transform; Goodness-of-fit measures; Log-cumulants; Hotelling’s $$T^2$$ T 2 statistic; 62Fxx; 60Exx; 43A43 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10163-9

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