The Geometric Birnbaum–Saunders regression model with cure rate

Cancho, Vicente G.; Louzada, Francisco; Barriga, Gladys Dorotea Cacsire

doi:10.1016/j.jspi.2011.11.007

Cited by 29 publications

(20 citation statements)

References 18 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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“…An immediate extension of this model is to consider the effects of covariates for each subject and also a possible heterogeneity between them. As an alternative to the Poisson-exponential distribution other distributions, such as Weibull-geometric [3], beta-Weibull geometric [9], Geometric Birnbaum-Saunders [5], can be considered for modeling. These issues are of interest and will be investigated in future.…”

Section: Final Commentsmentioning

confidence: 99%

The Poisson-exponential model for recurrent event data: an application to bowel motility data

Louzada

Macera²,

Cancho

2015

Journal of Applied Statistics

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This paper presents a new parametric model for recurrent events, in which the time of each recurrence is associated to one or multiple latent causes and no information is provided about the responsible cause for the event. This model is characterized by a rate function and it is based on the Poisson-exponential distribution, namely the distribution of the maximum among a random number (truncated Poisson distributed) of exponential times. The time of each recurrence is then given by the maximum lifetime value among all latent causes. Inference is based on a maximum likelihood approach. A simulation study is performed in order to observe the frequentist properties of the estimation procedure for small and moderate sample sizes. We also investigated likelihood-based tests procedures. A real example from a gastroenterology study concerning small bowel motility during fasting state is used to illustrate the methodology. Finally, we apply the proposed model to a real data set and compare it with the classical Homogeneous Poisson model, which is a particular case.

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“…It is straightforward. Cancho et al (2012) proposed and studied the geometric Birnbaum-Saunders regression with cure rate. However, they considered C(θ) = (1 − θ) −1 instead of C(θ) = θ(1 − θ) −1 .…”

Section: Birnbaum-saunders Geometric Distributionmentioning

confidence: 99%

A new class of fatigue life distributions

Bourguignon¹,

Silva²,

Cordeiro³

2013

Journal of Statistical Computation and Simulation

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In this paper, we introduce the Birnbaum-Saunders power series class of distributions which is obtained by compounding Birnbaum-Saunders and power series distributions. The new class of distributions has as a particular case the two-parameter Birnbaum-Saunders distribution. The hazard rate function of the proposed class can be increasing and upside-down bathtub shaped. We provide important mathematical properties such as moments, order statistics, estimation of the parameters and inference for large sample. Three special cases of the new class are investigated with some details. We illustrate the usefulness of the new distributions by means of two applications to real data sets.

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The Geometric Birnbaum–Saunders regression model with cure rate

Cited by 29 publications

References 18 publications

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

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

The Poisson-exponential model for recurrent event data: an application to bowel motility data

A new class of fatigue life distributions

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