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, Carlos Martin-Barreiro

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number1891
JournalMathematics
Volume9
Issue number16
DOIs
StatePublished - 2 Aug 2021
Externally publishedYes

Keywords

  • Birnbaum–saunders distribution
  • Data science
  • Estimation of moments and maximum likelihood
  • Monte carlo method
  • Polynomial functions
  • Proportionate-effect law
  • R software

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