Cumulative damage and times of occurrence for a multicomponent system: A discrete time approach

Fierro, Raúl; Leiva, Víctor; Maidana, Jean Paul

doi:10.1016/j.jmva.2018.08.004

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…Moreover, one of the objectives of this paper is to provide tools allowing us to carry out asymptotic inference on the parameters of the model. An article aiming at this objective, based on discrete-time models, was published in Fierro et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Cumulative damage for multi-type epidemics and an application to infectious diseases

Fierro

2023

J. Math. Biol.

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A continuous time multivariate stochastic model is proposed for assessing the damage of a multi-type epidemic cause to a population as it unfolds. The instants when cases occur and the magnitude of their injure are random. Thus, we define a cumulative damage based on counting processes and a multivariate mark process. For a large population we approximate the behavior of this damage process by its asymptotic distribution. Also, we analyze the distribution of the stopping times when the numbers of cases caused by the epidemic attain levels beyond certain thresholds. We focus on introducing some tools for statistical inference on the parameters related with the epidemic. In this regard, we present a general hypothesis test for homogeneity in epidemics and apply it to data of Covid-19 in Chile.

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Section: Introductionmentioning

confidence: 99%

Cumulative damage for multi-type epidemics and an application to infectious diseases

Fierro

2023

J. Math. Biol.

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“…The recent article by Aykroyd et al 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, and applications of multivariate Birnbaum‐Saunders distributions in spatial modeling appeared in the works of Garcia‐Papani et al 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…”

Section: Introductionmentioning

confidence: 99%

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

Leiva

Aykroyd

Marchant

2018

Appl Stoch Models Bus & Ind

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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

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“…Aykroyd et al published recently a review on multivariate BS distributions with some applications. In addition, cumulative damage models and their relation to times of occurrence were recently modeled in a multivariate setting for multicomponent systems by Fierro et al…”

Section: Introductionmentioning

confidence: 99%

Discussion of “Birnbaum‐Saunders distribution: A review of models, analysis, and applications” and a novel financial extreme value data analytics from natural disasters

Leiva

Lillo

Gomes

et al. 2018

Appl Stoch Models Bus & Ind

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The univariate Birnbaum-Saunders (BS) distribution was first postulated to model failure times in material science (see the work of Birnbaum and Saunders 1 ). In this modeling, a cumulative damage exceeds a threshold to produce the failure (see the work of Leiva and Saunders 2 ). The univariate BS distribution is unimodal, positively skewed (although close to a symmetric distribution in some cases), supported over a positive range of values and possessor of diverse and attractive properties (see the book of Johnson et al 3 ). The univariate BS distribution has been extensively studied and applied (see the works of Leiva et al 4,5 ). Most of its mathematical and statistical results until 2016 were published in the book of Leiva. 6 Multivariate BS distributions were derived as a natural extension to the univariate case, based on mathematical methods, with no fatigue theoretical arguments, different to the univariate BS distribution. Aykroyd et al 7 published recently a review on multivariate BS distributions with some applications. In addition, cumulative damage models and their relation to times of occurrence were recently modeled in a multivariate setting for multicomponent systems by Fierro et al. 8 Balakrishnan and Kundu 9 conducted a complete and interesting review of the BS distribution, which considered physical justifications, mathematical and statistical issues, shape analysis and links to other models, as well as formulations and generalizations for the univariate case. Furthermore, extensions to multivariate and matrix-variate versions of the BS distribution were also included. This review provides a full and updated list of references on the topic. However, in the book of Leiva 6 and in the review of Balakrishnan and Kundu, 9 no attention was paid to an extreme value BS (EVBS) distribution, which has several attractive properties and a different conception with respect to its standard version. Indeed, the standard BS distribution cannot be obtained as a particular case of the EVBS distribution, as it happens with other generalizations and extensions of the BS distribution.There are several reasons to justify the use of the BS distribution in the modeling of data with heavy tails. In particular, the EVBS distribution developed by Ferreira et al 10 provides some of these justifications. The EVBS distribution is based on the generalized extreme value (GEV) distribution. As mentioned, the standard BS distribution was derived to solve a problem of material fatigue, but the BS distribution has been also used to solve problems in areas as diverse as environment, finance, and medicine, where heavy-tailed phenomena are often detected. This kind of phenomena is frequently described by extreme value models. Then, the EVBS distribution can be a good alternative to BS distributions because of its good properties to model heavy-tailed phenomena.We discuss some aspects of the BS distribution reviewed by Balakrishnan and Kundu 9 and delve into the EVBS distribution, considering its features, modeling properties, and ne...

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Cumulative damage and times of occurrence for a multicomponent system: A discrete time approach

Cited by 4 publications

References 11 publications

Cumulative damage for multi-type epidemics and an application to infectious diseases

Cumulative damage for multi-type epidemics and an application to infectious diseases

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

Discussion of “Birnbaum‐Saunders distribution: A review of models, analysis, and applications” and a novel financial extreme value data analytics from natural disasters

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