Inference for the Birnbaum–Saunders Lifetime Regression Model with Applications

Zhu, Xiaojun

doi:10.1080/03610918.2013.844838

Cited by 12 publications

(9 citation statements)

References 23 publications

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“…The Birnbaum‐Saunders (BS) distribution as well as its respective regression models have been widely used in several fields, such as business, finance, insurance, management, and production (see the work of Leiva). There are at least three different modeling approaches in the BS context, which were introduced by Rieck and Nedelman, Leiva et al, and Balakrishnan and Zhu . A common point in these regression models is that the presence of correlation is not considered, despite the fact that it is relatively common.…”

Section: Discussionmentioning

confidence: 99%

Discussion of “Birnbaum‐Saunders distribution: A review of models, analysis, and applications” by N. Balakrishnan and Debasis Kundu

Saulo

Leão

Santos‐Neto

2018

Appl Stoch Models Bus & Ind

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The Birnbaum-Saunders (BS) distribution as well as its respective regression models have been widely used in several fields, such as business, finance, insurance, management, and production (see the work of Leiva 1 ). There are at least three different modeling approaches in the BS context, which were introduced by Rieck and Nedelman, 2 Leiva et al, 3 and Balakrishnan and Zhu. 4 A common point in these regression models is that the presence of correlation is not considered, despite the fact that it is relatively common. Therefore, the objective in this discussion is to fill this gap with the introduction of a BS time series model that allows the inclusion of a regression structure. Moreover, this discussion brings a relatively little explored point in the context of BS models, which is the area of time series. Some recent studies on BS time series models are discussed in the works of Saulo et al 5 and Rahul et al. 6 The proposed model is specified in terms of a time-varying conditional mean and can be thought of as an extension of the reparameterized BS (RBS) regression model proposed by Leiva et al. 3 An example with simulated data is provided to illustrate the proposed methodology. ORCIDHelton Saulo http://orcid.org/0000-0002-4467-8652 Jeremias Leão http://orcid.org/0000-0003-1176-0198 Manoel Santos-Neto

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Section: Discussionmentioning

confidence: 99%

Discussion of “Birnbaum‐Saunders distribution: A review of models, analysis, and applications” by N. Balakrishnan and Debasis Kundu

Saulo

Leão

Santos‐Neto

2018

Appl Stoch Models Bus & Ind

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“…In general, the results have shown that the proposed bimodal Birnbaum-Saunders distribution outperforms some existing models in the literature. As part of future research, it is of interest to study univariate and multivariate bimodal Birnbaum-Saunders regression models; see Rieck and Nedelman (1991), Balakrishnan and Zhu (2015) and Marchant et al (2016). Moreover, time series models based on the bimodal Birnbaum-Saunders distribution with corresponding influence diagnostic tools can also be considered; see Saulo et al (2017).…”

Section: Discussionmentioning

confidence: 99%

On a bimodal Birnbaum-Saunders distribution with applications to lifetime data

Vila,

Leão,

Saulo

et al. 2018

Preprint

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The Birnbaum-Saunders distribution is a flexible and useful model which has been used in several fields. In this paper, a new bimodal version of this distribution based on the alpha-skew-normal distribution is established. We discuss some of its mathematical and inferential properties. We consider likelihood-based methods to estimate the model parameters. We carry out a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators. For illustrative purposes, three real data sets are analyzed. The results indicated that the proposed model outperformed some existing models in the literature, in special, a recent bimodal extension of the Birnbaum-Saunders distribution.

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“…Then, for the BS d distribution we are also going to consider its associated regression model, which will be the goal of this part of the study. The associated BS d regression model that we are going to introduce is inspired by continuous BS regression model developed by Balakrishnan and Zhu (2015), where they considered the scale parameter depending on covariates.…”

Section: Discrete Birnbaum-saunders Regression Modelmentioning

confidence: 99%

Theoretical results and modeling under the discrete Birnbaum-Saunders distribution

Vilca¹,

Vila²,

Saulo³

et al. 2022

Preprint

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In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability and order statistics are also presented.In addition, we propose a regression model based on the discrete Birnbaum-Saunders distribution. The model parameters are estimated by the maximum likelihood method and a Monte Carlo study is performed to evaluate the performance of the estimators. Finally, we illustrate the proposed methodology with the use of real data sets.

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Inference for the Birnbaum–Saunders Lifetime Regression Model with Applications

Cited by 12 publications

References 23 publications

Discussion of “Birnbaum‐Saunders distribution: A review of models, analysis, and applications” by N. Balakrishnan and Debasis Kundu

Discussion of “Birnbaum‐Saunders distribution: A review of models, analysis, and applications” by N. Balakrishnan and Debasis Kundu

On a bimodal Birnbaum-Saunders distribution with applications to lifetime data

Theoretical results and modeling under the discrete Birnbaum-Saunders distribution

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