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

Jimmy Reyes, Jaime Arrué, Víctor Leiva and Carlos Martin-Barreiro
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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

Mathematics, 2021, vol. 9, issue 16, 1-19

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.

Keywords: Birnbaum–Saunders distribution; data science; estimation of moments and maximum likelihood; Monte Carlo method; polynomial functions; proportionate-effect law; R software (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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