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Statistical Inference for a General Family of Modified Exponentiated Distributions

Author

Listed:
  • 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
    These authors contributed equally to this work.)

  • Yuri A. Iriarte

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 02800, Chile
    These authors contributed equally to this work.)

  • Yolanda M. Gómez

    (Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
    These authors contributed equally to this work.)

  • Inmaculada Barranco-Chamorro

    (Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, Spain
    These authors contributed equally to this work.)

  • Héctor W. Gómez

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 02800, Chile
    These authors contributed equally to this work.)

Abstract

In this paper, a modified exponentiated family of distributions is introduced. The new model was built from a continuous parent cumulative distribution function and depends on a shape parameter. Its most relevant characteristics have been obtained: the probability density function, quantile function, moments, stochastic ordering, Poisson mixture with our proposal as the mixing distribution, order statistics, tail behavior and estimates of parameters. We highlight the particular model based on the classical exponential distribution, which is an alternative to the exponentiated exponential, gamma and Weibull. A simulation study and a real application are presented. It is shown that the proposed family of distributions is of interest to applied areas, such as economics, reliability and finances.

Suggested Citation

  • Emilio Gómez-Déniz & Yuri A. Iriarte & Yolanda M. Gómez & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2021. "Statistical Inference for a General Family of Modified Exponentiated Distributions," Mathematics, MDPI, vol. 9(23), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3069-:d:690811
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    References listed on IDEAS

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