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Inflated Unit-Birnbaum-Saunders Distribution

Author

Listed:
  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

  • Roger Tovar-Falón

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

  • Carlos Barrera-Causil

    (Grupo de Investigación Davinci, Facultad de Ciencias Exactas y Aplicadas, Instituto Tecnológico Metropolitano, Medellín 050034, Colombia
    These authors contributed equally to this work.)

Abstract

The modeling different data behaviour like the human development index as a function of life expectancy, the water capacity of a reservoir with respect to a certain threshold, or the percentage of death rate of an infant before his or her first birthday, are situations which a researcher can face. It is noteworthy that these problems may have in common data with excessive zeros and ones. Then, it is essential to have flexible and accuracy models to fit data with these features. Given the relevance of data modeling with excessive zeros and ones, in this paper, a mixture of discrete and continuous distributions is proposed for modeling data with these behaviors. Additionally, the Unit-Birnbaum-Saunders distribution is considered with the aim to explain the continuous component of the model and the features of a Bernoulli process. The estimation of the parameters is based on the maximum likelihood method. Observed and expected information matrices are derived, illustrating interesting aspects of the likelihood approach. Finally, with practical applications by using real data we can show the advantage of using our proposal concerning the inflated beta model.

Suggested Citation

  • Guillermo Martínez-Flórez & Roger Tovar-Falón & Carlos Barrera-Causil, 2022. "Inflated Unit-Birnbaum-Saunders Distribution," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:667-:d:754340
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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