Scale Mixture of Gleser Distribution with an Application to Insurance Data-Reference-Cited by-同舟云学术

Scale Mixture of Gleser Distribution with an Application to Insurance Data

Published:2024-05-03 Issue:9 Volume:12 Page:1397
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Olmos Neveka M.¹^ORCID,Gómez-Déniz Emilio²^ORCID,Venegas Osvaldo³^ORCID

Affiliation:

1. Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

2. Department of Quantitative Methods in Economics, 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

Abstract

In this paper, the scale mixture of the Gleser (SMG) distribution is introduced. This new distribution is the product of a scale mixture between the Gleser (G) distribution and the Beta(a,1) distribution. The SMG distribution is an alternative to distributions with two parameters and a heavy right tail. We study its representation and some basic properties, maximum likelihood inference, and Fisher’s information matrix. We present an application to a real dataset in which the SMG distribution shows a better fit than two other known distributions.

Funder

Semillero

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/9/1397/pdf

Reference28 articles.

1. Pareto, V. (1897). Cours d’Éconimie Politique, Librairie Droz.

2. Beirlant, J., Teugels, J.L., and Vynckier, P. (1996). Practical Analysis of Extreme Values, Leuven University Press.

3. Generalized Pareto fit to the society of actuaries’ large claims database;Beirlant;N. Am. Actuar. J.,2004

4. Discussion of the Danish data on large fire insurance losses;Resnick;ASTIN Bull.,1997

5. Johnson, N.L., Kotz, S., and Balakrishnan, N. (1995). Continuous Univariate Distributions, Wiley. [2nd ed.].