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.
Highlights
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Many phenomena may be modeled by continuous statistical distributions [1]
Note that the empirical bias becomes smaller as the sample size n increases, as expected
Summary
Citation: Reyes, J.; Arrué, J.; Leiva, V.; Martin-Barreiro, C. A New and Carlos Martin-Barreiro 3,4 Escuela de Ingeniería Industrial, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile Facultad de Ingeniería, Universidad Espíritu Santo, Samborondón 0901952, Ecuador
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