A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data

Neveka M. Olmos, Emilio Gómez-Déniz, Osvaldo Venegas () and Héctor W. Gómez
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Neveka M. Olmos: Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Emilio Gómez-Déniz: Department of Quantitative Methods in Economics and TIDES Institute, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain
Osvaldo Venegas: Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
Héctor W. Gómez: Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2024, vol. 12, issue 11, 1-17

Abstract: The half-normal distribution is composited with the Pareto model to obtain a uni-parametric distribution with a heavy right tail, called the composite half-normal-Pareto distribution. This new distribution is useful for modeling positive data with atypical observations. We study the properties and the behavior of the right tail of this new distribution. We estimate the parameter using a method based on percentiles and the maximum likelihood method and assess the performance of the maximum likelihood estimator using Monte Carlo. We report three applications, one with simulated data and the others with income and expenditure data, in which the new distribution presents better performance than the Pareto distribution.

Keywords: half-normal distribution; heavy-tailed distribution; maximum likelihood; VaR (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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