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A New Birnbaum–Saunders Distribution and Its Mathematical Features Applied to Bimodal Real-World Data from Environment and Medicine

Author

Listed:
  • Jimmy Reyes

    (Departamento de Matemáticas, Universidad de Antofagasta, Antofagasta 1270300, Chile)

  • Jaime Arrué

    (Departamento de Matemáticas, Universidad de Antofagasta, Antofagasta 1270300, Chile)

  • Víctor Leiva

    (Escuela de Ingeniería Industrial, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Carlos Martin-Barreiro

    (Facultad de Ciencias Naturales y Matemáticas, Universidad Politécnica ESPOL, Guayaquil 090902, Ecuador
    Facultad de Ingeniería, Universidad Espíritu Santo, Samborondón 0901952, Ecuador)

Abstract

In this paper, we propose and derive a Birnbaum–Saunders distribution to model bimodal data. This new distribution is obtained using the product of the standard Birnbaum–Saunders distribution and a polynomial function of the fourth degree. We study the mathematical and statistical properties of the bimodal Birnbaum–Saunders distribution, including probabilistic features and moments. Inference on its parameters is conducted using the estimation methods of moments and maximum likelihood. Based on the acceptance–rejection criterion, an algorithm is proposed to generate values of a random variable that follows the new bimodal Birnbaum–Saunders distribution. We carry out a simulation study using the Monte Carlo method to assess the statistical performance of the parameter estimators. Illustrations with real-world data sets from environmental and medical sciences are provided to show applications that can be of potential use in real problems.

Suggested Citation

  • Jimmy Reyes & Jaime Arrué & Víctor Leiva & Carlos Martin-Barreiro, 2021. "A New Birnbaum–Saunders Distribution and Its Mathematical Features Applied to Bimodal Real-World Data from Environment and Medicine," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1891-:d:611030
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    References listed on IDEAS

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