A versatile family of heavy-tail distributions: Beyond the Weibull model with applications

Abstract

A simple integral expression for the Catalan constant serves as the starting point of this work, leading to a family of continuous probability distributions with broad versatility. A particular case of this distribution, connected to the Weibull distribution, is studied in detail. For this distribution, some properties are explored, and analytical expressions are obtained for the cumulative distribution function, moments, moment generating function, and so on. Furthermore, a particular distribution is a special case of the subexponential class, and consequently, the proposed distribution has heavy-tails. The normal equations for deriving maximum likelihood estimators are detailed, and a simulation study is conducted. Several applications lead us to conclude that this distribution performs similarly to, but slightly better than, the Weibull distribution, and much better than other classical distributions, such as the gamma, inverse Gaussian, and lognormal distributions.

Keywords

• ArcTan function
• heavy-tail
• subexponential
• Weibull distribution

Supporting Institution

EGD was partially funded by grant PID2021-127989OB-I00 (Ministerio de Ciencia, Innovación y Universidades, Spain). JMS acknowledges financial Support from the I+D+i project Ref. PID2024-156871NB-I00 financed by MICIU/AEI/10.13039/501100011033/FEDER,UE.

Project Number

PID2021-127989OB-I00

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