Some generalisations of Birnbaum-Saunders and sinh-normal distributions

Narro, Antonio; inguez-Molina, Jose Ramon Dom ́

doi:10.12988/imf.2006.06146

Cited by 34 publications

(15 citation statements)

References 24 publications

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“…Several different models relating to univariate and multivariate BS distributions can be found in the works of Athayde et al, Balakrishnan and Saulo, Barros et al, Bhatti, Cancho et al, Cordeiro et al, Cordeiro and Lemonte, Desmond et al, Díaz‐García and Domínguez‐Molina, Díaz‐García and Leiva, Ferreira et al, Fierro et al, Fonseca and Cribari‐Neto, Genç, Gomes et al, Guiraud et al, Gupta and Akman, Hashimoto et al, Jamalizadeh and Kundu, Khosravi et al, Kundu, Leiva et al, Lemonte and Cordeiro, Lemonte and Ferrari, Martínez‐Flórez et al, Marchant et al, Olmos et al, Onar and Padgett, Ortega et al, Owen, Owen and Padgett, Park and Padgett, Patriota, Pescim et al, Pourmousa et al, Raaijmakers, Romeiro et al, Reina et al, Reyes et al, Sanhueza et al, Vilca and Leiva‐Sánchez, Volodin and Dzhungurova, and Ziane et al Recently, some survival analytic methods have been developed based on BS and related models. For example, one may refer to the works of Leão, Leão et al, and Balakrishnan and Liu .…”

Section: Concluding Remarks and Further Readingmentioning

confidence: 99%

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

106

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Birnbaum and Saunders introduced a two-parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix-variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research. KEYWORDSBayes estimators, EM algorithm, Fisher information matrix, hazard function, length-biased distribution, moments and inverse moments, probability density function, stochastic orderings, TP 2 property 4

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Section: Concluding Remarks and Further Readingmentioning

confidence: 99%

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

106

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“…The generalized Birnbaum-Saunders distribution considered in this paper was introduced by Dıaz-Garcıa and Domınguez-Molina (2006). They obtained it by adding a second shape parameter to the BS distribution function.…”

Section: The Bimodal Birnbaum-saunders Distributionmentioning

confidence: 99%

A new log-linear bimodal Birnbaum–Saunders regression model with application to survival data

Cribari‐Neto¹,

Fonseca²

2019

Braz. J. Probab. Stat.

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The log-linear Birnbaum-Saunders model has been widely used in empirical applications. We introduce an extension of this model based on a recently proposed version of the Birnbaum-Saunders distribution which is more flexible than the standard Birnbaum-Saunders law since its density may assume both unimodal and bimodal shapes. We show how to perform point estimation, interval estimation and hypothesis testing inferences on the parameters that index the regression model we propose. We also present a number of diagnostic tools, such as residual analysis, local influence, generalized leverage, generalized Cook's distance and model misspecification tests. We investigate the usefulness of model selection criteria and the accuracy of prediction intervals for the proposed model. Results of Monte Carlo simulations are presented. Finally, we also present and discuss an empirical application.

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“…The r.v. Y = log(T ) follows a sinhyperbolic-spherical distribution or log-GBS distribution, which was studied by Díaz-García and Domínguez-Molina (2006) and it is important for log-linear regression analysis. In addition, the parameter estimates, moments, and random numbers can be obtained efficiently from the distribution of Y.…”

Section: Characterization and Propertiesmentioning

confidence: 99%

Generalized Birnbaum‐Saunders distributions applied to air pollutant concentration

et al. 2007

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SUMMARYThe generalized Birnbaum-Saunders (GBS) distribution is a new class of positively skewed models with lighter and heavier tails than the traditional Birnbaum-Saunders (BS) distribution, which is largely applied to study lifetimes. However, the theoretical argument and the interesting properties of the GBS model have made its application possible beyond the lifetime analysis. The aim of this paper is to present the GBS distribution as a useful model for describing pollution data and deriving its positive and negative moments. Based on these moments, we develop estimation and goodness-of-fit methods. Also, some properties of the proposed estimators useful for developing asymptotic inference are presented. Finally, an application with real data from Environmental Sciences is given to illustrate the methodology developed. This example shows that the empirical fit of the GBS distribution to the data is very good. Thus, the GBS model is appropriate for describing air pollutant concentration data, which produces better results than the lognormal model when the administrative target is determined for abating air pollution.

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Some generalisations of Birnbaum-Saunders and sinh-normal distributions

Cited by 34 publications

References 24 publications

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

A new log-linear bimodal Birnbaum–Saunders regression model with application to survival data

Generalized Birnbaum‐Saunders distributions applied to air pollutant concentration

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