A new extension of the Birnbaum–Saunders distribution

Lemonte, Artur J.

doi:10.1214/11-bjps160

Cited by 42 publications

(16 citation statements)

References 33 publications

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“…Some new distributions using Eq. (57) have been proposed by taking the base distribution F ( x ) to be extended Weibull,137 normal,138 and Birnbaum‐Saunders distributions 139. For a thorough discussion and review of life distributions, one may refer to the book by Marshall and Olkin 140…”

Section: Methods Of Adding Parametersmentioning

confidence: 99%

Methods for generating families of univariate continuous distributions in the recent decades

Lee

Famoye

Alzaatreh

2013

WIREs Computational Stats

150

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There has been a renewed interest in developing more flexible statistical distributions in recent decades. A major milestone in the methods for generating statistical distributions is undoubtedly the system of differential equation approach. There is a recent renewed interest in generating skewed distributions. Generally speaking, the methods developed prior to 1980s may be summarized into three categories: (1) method of differential equation, (2) method of transformation, and (3) quantile method. Techniques developed since 1980s may be categorized as ‘methods of combination’ for the reason that these methods attempt to combine existing distributions into new distributions or adding new parameters to an existing distribution. This article discusses five general methods of combination and their variations. These five are (1) method of generating skew distributions, (2) method of adding parameters (e.g., exponentiation), (3) beta generated method, (4) transformed‐transformer method, and (5) composite method. WIREs Comput Stat 2013, 5:219–238. doi: 10.1002/wics.1255 This article is categorized under: Algorithms and Computational Methods > Random Number Generation Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

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Section: Methods Of Adding Parametersmentioning

confidence: 99%

Methods for generating families of univariate continuous distributions in the recent decades

Lee

Famoye

Alzaatreh

2013

WIREs Computational Stats

150

View full text Add to dashboard Cite

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“…For different inference‐related issues, one may refer to the works of Ahmed et al, Arellano‐Valle et al, Athayde et al, Audrey et al, Azevedo et al, Balakrishnan et al, Balakrishnan and Zhu, Barros et al, Chang and Tang, Cordeiro et al, Cysneiros et al, Desmond and Yang, Farias and Lemonte, Guo et al, Jeng, Lachos et al, Lemonte, Lemonte and Cordeiro, Lemonte et al, Lemonte and Ferrari, Lemonte and Patriota, Li et al, Li and Xu, Lillo et al, Lu and Chang, Meintanis, Moala et al, Niu et al, Padgett and Tomlinson, Pérez and Correa, Qu and Xie, Riquelme et al, Sánchez et al, Santana et al, Santos‐Neto et al, Saulo et al, Sha and Ng, Teimouri et al, Tsionas, Upadhyay and Mukherjee, Vanegas and Paula, Vanegas et al, Vilca et al, Wang, Wang and Fei, Wang et al, Xiao et al, Xie and Wei, Xu and Tang, Xu et al, Zhu and Balakrishnan, and the references cited therein.…”

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

111

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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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“…A life distribution known as Birnbaum-Saunders (BS) has received considerable attention due to its good properties. Because of its genesis from fatigue of materials, the BS distribution has been largely applied to engineering, but recent applications range across diverse fields as biology, business, environment and industry, which have been conducted by an international, transdisciplinary group of researchers; see, for example, Bhatti (2010), Leiva et al (2011Leiva et al ( , 2014aLeiva et al ( ,b,c, 2015aLeiva et al ( ,b, 2016aLeiva et al ( ,b, 2017, Villegas et al (2011), Santana et al (2011), Ferreira et al (2012), Paula et al (2012), Lemonte (2013), Marchant et al (2013), Saulo et al (2013Saulo et al ( , 2018, Kundu (2015b), Sánchez et al (2015), Wanke and Leiva (2015), Santos-Neto et al (2016), Vanegas and Paula (2016), Bourguignon et al (2017), Desousa et al (2017), Garcia-Papani et al (2017), Leão et al (2017a,b,c) and Lillo et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Failure rate of Birnbaum–Saunders distributions: Shape, change-point, estimation and robustness

Athayde¹,

Azevedo²,

Barros³

et al. 2019

Braz. J. Probab. Stat.

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The Birnbaum-Saunders (BS) distribution has been largely studied and applied. A random variable with BS distribution is a transformation of another random variable with standard normal distribution. Generalized BS distributions are obtained when the normally distributed random variable is replaced by another symmetrically distributed random variable. This allows us to obtain a wide class of positively skewed models with lighter and heavier tails than the BS model. Its failure rate admits several shapes, including the unimodal case, with its change-point being able to be used for different purposes. For example, to establish the reduction in a dose, and then in the cost of the medical treatment. We analyze the failure rates of generalized BS distributions obtained by the logistic, normal and Student-t distributions, considering their shape and change-point, estimating them, evaluating their robustness, assessing their performance by simulations, and applying the results to real data from different areas.Special cases of the t distribution are the Cauchy and normal distributions, when ν = 1 and ν → +∞, respectively.

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A new extension of the Birnbaum–Saunders distribution

Cited by 42 publications

References 33 publications

Methods for generating families of univariate continuous distributions in the recent decades

Methods for generating families of univariate continuous distributions in the recent decades

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

Failure rate of Birnbaum–Saunders distributions: Shape, change-point, estimation and robustness

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