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A New Family of Distributions Based on Proportional Hazards

Author

Listed:
  • 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)

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.

Suggested Citation

  • Guillermo Martínez-Flórez & Carlos Barrera-Causil & Osvaldo Venegas & Heleno Bolfarine & Héctor W. Gómez, 2022. "A New Family of Distributions Based on Proportional Hazards," Mathematics, MDPI, vol. 10(3), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:378-:d:734424
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    References listed on IDEAS

    as
    1. Arthur Pewsey, 2000. "Problems of inference for Azzalini's skewnormal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 859-870.
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