Discussion of “Birnbaum‐Saunders distribution: A review of models, analysis, and applications” and a novel multivariate data analytics for an economics example in the textile industry

Abstract

The fifty years since the birth of the Birnbaum-Saunders distribution can be broken down into three distinct periods. The first 30 years showed slow development and few applications; see for example other works. 1-4 The next ten years (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010), in contrast, represented rapid methodological development in terms of estimation, diagnostics, and computational aspects, as well as generalizations and novel modeling based on arguments of cumulative effects; see, for example the works of Volodin and Dzhungurova, 5 Galea et al, 6 and Vilca et al. 7 Work during the most recent period (2011 to the present) is characterized by the breaking of the previously ever-present link with lifetime modeling and the resultant move to new areas of application such as agriculture, business, econometrics, environment, industry, management, medicine, neurology, and seismology; see the book by Leiva 8 for details of these developments and applications of the univariate Birnbaum-Saunders distribution. Leiva, 8 however, does not emphasize multivariate versions of the Birnbaum-Saunders distribution.In their paper, Balakrishnan and Kundu 9 conducted a comprehensive review of the Birnbaum-Saunders distribution, which includes mathematical and statistical properties, physical interpretations, analysis of the distribution shape, relations with other distributions, regression modeling and generalizations of the univariate case, and extensions to the multivariate and matrix-variate cases. Our discussion updates and complements the references on the topic. We also provide more details on multivariate Birnbaum-Saunders models and discuss a novel application in economics.The recent article by Aykroyd et al 10 also includes a review of multivariate Birnbaum-Saunders distributions and applications. Work on multivariate Birnbaum-Saunders models and their applications was presented by Marchant et al, [11][12][13] and applications of multivariate Birnbaum-Saunders distributions in spatial modeling appeared in the works of In addition, multivariate cumulative damage models and their relationship with time of occurrence in the context of multicomponent systems were recently derived by Fierro et al. 17 In our discussion, we provide further aspects of the multivariate Birnbaum-Saunders distribution reviewed by Balakrishnan and Kundu, 9 considering its properties and features, modeling, and diagnostics, as well as new opportunities and future applications. 112

Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model

“…The bivariate version of the BS distribution was proposed in [30], where ML and modified moment estimates of the corresponding parameters were derived. Multivariate log-BS distributions and multivariate BS log-linear regression models are presented in [10,12,[31][32][33].…”

Birnbaum‐Saunders quantile regression and its diagnostics with application to economic data

“…651‐663) , and Leiva 3 . Although the BS distribution has its origins in physics and engineering, it has also received interest in several other areas, including, but no limited to, business, earth sciences, industry and medicine; for details, see References 4‐20. The study of the BS distribution has received growing interest and a considerable amount of work is available; see the recent publications by Leiva, 3 Balakrishnan and Kundu, 21 and references therein, which summarize most of the works to the date.…”

Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data

“…Its natural applications have been mainly focused on engineering. However, today they range diverse fields including air pollution [4,5], business [6], earth sciences [7,8], industry [9,10], and medicine [11,12], among other areas. These applications have been performed by an international transdisciplinary group of researchers.…”