The Gauss hypergeometric Gleser distribution with applications to flood peaks exceedance and income data

Neveka M. Olmos; Emilio Gómez-Déniz; Osvaldo Venegas; Neveka M. Olmos; Emilio Gómez-Déniz; Osvaldo Venegas

doi:10.3934/math.2025611

AIMS Mathematics

2025, Volume 10, Issue 6: 13575-13593. doi: 10.3934/math.2025611

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The Gauss hypergeometric Gleser distribution with applications to flood peaks exceedance and income data

1.
Departamento de Estadística y Ciencia de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
2.
Department of Quantitative Methods in Economics and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain
3.
Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile

Received: 14 March 2025 Revised: 17 May 2025 Accepted: 04 June 2025 Published: 13 June 2025
MSC : 62E15, 62E20, 62P12

We introduced the Gauss hypergeometric Gleser (GHG) distribution, a novel extension of the Gleser (G) distribution that unifies families of Gleser distributions. We studied their representations and some basic properties and showed that the GHG distribution is heavy-tailed. The maximum likelihood method is used for parameter estimation, and the Fisher information matrix derived. We assessed the performance of the maximum likelihood estimators via Monte Carlo simulations. Moreover, we present applications to two data sets in which the GHG distribution shows a better fit than other known distributions.
- Gleser distribution,
- heavy-tailed distribution,
- scale mixture,
- maximum likelihood,
- Gauss hypergeometric function
Citation: Neveka M. Olmos, Emilio Gómez-Déniz, Osvaldo Venegas. The Gauss hypergeometric Gleser distribution with applications to flood peaks exceedance and income data[J]. AIMS Mathematics, 2025, 10(6): 13575-13593. doi: 10.3934/math.2025611

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Abstract

We introduced the Gauss hypergeometric Gleser (GHG) distribution, a novel extension of the Gleser (G) distribution that unifies families of Gleser distributions. We studied their representations and some basic properties and showed that the GHG distribution is heavy-tailed. The maximum likelihood method is used for parameter estimation, and the Fisher information matrix derived. We assessed the performance of the maximum likelihood estimators via Monte Carlo simulations. Moreover, we present applications to two data sets in which the GHG distribution shows a better fit than other known distributions.

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