Bimodal Birnbaum–Saunders distribution with applications to non negative measurements

Olmos, Neveka M.; Martínez-Flórez, Guillermo; Bolfarine, Heleno

doi:10.1080/03610926.2015.1133824

Cited by 19 publications

(26 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…λ is a parameter that controls asymmetry (skewness) and δ is a shape parameter related to bimodality of our proposal. If λ = 0 then we obtain, as a particular case, the model introduced by [22]. Figures 1 and 2 depict the behaviour of (8) for some values of parameters, illustrating that it can be bimodal for some combinations of them.…”

Section: Results In Flexible Birnbaum-saundersmentioning

confidence: 91%

“…Specifically, a closed expression for the cumulative distribution function (cdf) is given in terms of the cdf of a bivariate normal distribution. Some of the models proposed in [15,22] are obtained as particular cases. The shape and bimodality of the distribution are studied.…”

Section: Bs Modelmentioning

confidence: 99%

“…As initial estimates of α and β can be proposed the estimates of these parameters obtained in the basic BS model, denoted as α 0 and β 0 . These estimates can be plugged into (21) and (22) to obtain preliminar estimates of δ and λ, δ 0 and λ 0 , and so, start the recursion.…”

Section: Maximum Likelihood Estimatorsmentioning

confidence: 99%

See 2 more Smart Citations

Flexible Birnbaum–Saunders Distribution

et al. 2019

Self Cite

View full text Add to dashboard Cite

In this paper, we propose a bimodal extension of the Birnbaum-Saunders model by including an extra parameter. This new model is termed flexible Birnbaum-Saunders (FBS) and includes the ordinary Birnbaum-Saunders (BS) and the skew Birnbaum-Saunders (SBS) model as special cases. Its properties are studied. Parameter estimation is considered via an iterative maximum likelihood approach. Two real applications, of interest in environmental sciences, are included, which reveal that our proposal can perform better than other competing models.

show abstract

Section: Results In Flexible Birnbaum-saundersmentioning

confidence: 91%

Section: Bs Modelmentioning

confidence: 99%

See 1 more Smart Citation

Flexible Birnbaum–Saunders Distribution

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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

show abstract

“…Its null distribution is standard normal with error of order O(n −1 ). The score function and the observed information matrix, which can be found in [39], are used to obtain U 2 in the BBS model. The SLR bp test is based on 1,000 bootstrap samples.…”

Section: Consider the Random Variablementioning

confidence: 99%

Inference in a bimodal Birnbaum–Saunders model

Fonseca

Cribari‐Neto

2018

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

We address the issue of performing inference on the parameters that index a bimodal extension of the Birnbaum-Saunders distribution (BS). We show that maximum likelihood point estimation can be problematic since the standard nonlinear optimization algorithms may fail to converge. To deal with this problem, we penalize the log-likelihood function. The numerical evidence we present shows that maximum likelihood estimation based on such penalized function is made considerably more reliable. We also consider hypothesis testing inference based on the penalized log-likelihood function. In particular, we consider likelihood ratio, signed likelihood ratio, score and Wald tests. Bootstrap-based testing inference is also considered. We use a nonnested hypothesis test to distinguish between two bimodal BS laws. We derive analytical corrections to some tests. Monte Carlo simulation results and empirical applications are presented and discussed.

show abstract

Bimodal Birnbaum–Saunders distribution with applications to non negative measurements

Cited by 19 publications

References 33 publications

Flexible Birnbaum–Saunders Distribution

Flexible Birnbaum–Saunders Distribution

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

Inference in a bimodal Birnbaum–Saunders model

Contact Info

Product

Resources

About