A New Family of Distributions Based on Proportional Hazards

Guillermo Martínez-Flórez, Carlos Barrera-Causil, Osvaldo Venegas, Heleno Bolfarine and Héctor W. Gómez
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Guillermo Martínez-Flórez: Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad de Córdoba, Córdoba 2300, Colombia
Carlos Barrera-Causil: Facultad de Ciencias Exactas y Aplicadas, Instituto Tecnológico Metropolitano, Medellín 050034, Colombia
Osvaldo Venegas: Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
Heleno Bolfarine: Departamento de Estatística, Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo 05508-090, Brazil
Héctor W. Gómez: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2022, vol. 10, issue 3, 1-14

Abstract: In this article, we introduce a new family of symmetric-asymmetric distributions based on skew distributions and on the family of order statistics with proportional hazards. This new family of distributions is able to fit both unimodal and bimodal asymmetric data. Furthermore, it contains, as special cases, the symmetric distribution and the “skew-symmetric” family, and therefore the skew-normal distribution. Another interesting feature of the family is that the parameter controlling the distributional shape in bimodal cases takes values in the interval (0, 1); this is an advantage for computing maximum likelihood estimates of model parameters, which is performed by numerical methods. The practical utility of the proposed distribution is illustrated in two real data applications.

Keywords: bimodal distribution; power normal model; skew-normal distribution; skewness; kurtosis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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