Inference and optimal censoring schemes for progressively censored Birnbaum–Saunders distribution

Pradhan, Biswabrata; Kundu, Debasis

doi:10.1016/j.jspi.2012.11.007

Cited by 67 publications

(20 citation statements)

References 28 publications

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“…Pradhan and Kundu considered the inference for parameters α and β of the BS distribution when the data are Type‐II progressively censored. In a Type‐II progressive censoring experiment, the data are of the form {( t 1: m : n , R 1 ),…,( t m : m : n , R m )}.…”

Section: Point and Interval Estimation Based On Censored Samplesmentioning

confidence: 99%

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

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

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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: Point and Interval Estimation Based On Censored Samplesmentioning

confidence: 99%

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

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

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“…In case of Weibull and other lifetime distributions, most of the available criteria to find the OCS are based on the expected Fisher information matrix, ie, the asymptotic variance covariance matrix of the MLEs; see, for example, Ng et al, 13 Pradhan and Kundu, 14 Pradhan and Kundu, 15 Balakrishnan and Cramer, 2 and the references cited therein.…”

Section: Optimum Censoring Schemementioning

confidence: 99%

“…Censoring Scheme E(Vol 0.1 ) ETOT m = 25, k = 20, R = (5, 0 (18) ) 12.463 6.420 m = 25, k = 20, R = (0, 5, 0 (17) ) 12.583 6.383 m = 25, k = 20, R = (0 (2) , 5, 0 (16) ) 12.845 6.369 m = 25, k = 20, R = (0 (3) , 5, 0 (15) ) 13.032 6.245 m = 25, k = 20, R = (0 (4) , 5, 0 (14) ) 13.243 6.181 m = 25, k = 20, R = (0 (8) , 5, 0 (10) ) 14.614 6.043 m = 25, k = 20, R = (0 (14) , 5, 0 (4) ) 17.319 5.092 m = 25, k = 20, R = (0 (16) 19.895 2.523 m = 30, k = 25, R = (0 (5) , 5, 0 (18) ) 20.094 2.522 m = 30, k = 25, R = (0 (8) , 5, 0 (15) ) 20.665 2.488 m = 30, k = 25, R = (0 (12) , 5, 0 (11) ) 21.478 2.445 m = 30, k = 25, R = (0 (15) , 5, 0 (8) ) 22.538 2.374 m = 30, k = 25, R = (0 (18) , 5, 0 (5) ) 23.846 2.274 m = 30, k = 25, R = (0 (23) ,5)…”

Section: Tablementioning

confidence: 99%

“…Censoring Scheme E(Vol 0.1 ) ETOT m = 25, k = 20, R = (5, 0 (18) ) 49.927 1.523 m = 25, k = 20, R = (0, 5, 0 (17) ) 50.653 1.522 m = 25, k = 20, R = (0 (2) , 5, 0 (16) ) 51.265 1.515 m = 25, k = 20, R = (0 (3) , 5, 0 (15) ) 51.578 1.512 m = 25, k = 20, R = (0 (4) , 5, 0 (14) ) 52.719 1.508 m = 25, k = 20, R = (0 (8) , 5, 0 (10) ) 57.245 1.492 m = 25, k = 20, R = (0 (14) , 5, 0 (4) ) 67.359 1.424 m = 25, k = 20, R = (0 (16) = 2, 1 = 0.5, 2 = 1…”

Section: Tablementioning

confidence: 99%

“…, 5, 0(2) ) 20.768 4.458 m = 25, k = 20, R = (0(17) ,5,0) 20.918 3.884 m = 25, k = 20, R =( (18) ,5) 22.883 3.023 m = 30, k = 25, R = (5, 0 (23) ) 9.616 7.181 m = 30, k = 25, R = (0, 5, 0 (22) ) 9.718 7.145 m = 30, k = 25, R = (0 (2) , 5, 0 (21) ) 9.743 7.081 m = 30, k = 25, R = (0 (3) , 5, 0 (20) ) 9.834 7.074 m = 30, k = 25, R = (0 (5) , 5, 0 (18) ) 9.908 6.986 m = 30, k = 25, R = (0 (8) , 5, 0 (15) ) 10.304 6.954 m = 30, k = 25, R = (0(12) , 5, 0 (11) ) 10.680 6.675 m = 30, k = 25, R = (0(15) , 5, 0 (8) ) 11.217 6.454 m = 30, k = 25, R = (0 (18) , 5, 0 (5) ) 12.045 5.934 m = 30, k = 25, R = (0 (23) = 0.5, 2 = 1 Censoring Scheme E(Vol 0.1 ) ETOT m = 25, k = 20, R = (5, 0 (18) ) 24.360 2.393 m = 25, k = 20, R = (0, 5, 0 (17) ) 25.214 2.384 m = 25, k = 20, R = (0 (2) , 5, 0 (16) ) 25.524 2.374 m = 25, k = 20, R = (0 (3) , 5, 0 (15) ) 26.034 2.366 m = 25, k = 20, R = (0 (4) , 5, 0 (14) ) 26.513 2.359 m = 25, k = 20, R = (0 (8) , 5, 0 (10) ) 28.065 2.300 m = 25, k = 20, R = (0 (14) , 5, 0 (4) ) 36.513 2.120 m = 25, k = 20, R = (0 (16) , 5, 0 (2) ) 38.831 1.963 m = 25, k = 20, R = (0 (17) ,5,0) 40.552 1.816 m = 25, k = 20, R =(0 (18) ,5) 46.317 1.582 m = 30, k = 25, R = (5, 0 (23) ) 19.331 2.549 m = 30, k = 25, R = (0, 5, 0 (22) ) 19.414 2.536 m = 30, k = 25, R = (0 (2) , 5, 0 (21) ) 19.538 2.524 m = 30, k = 25, R = (0 (3) , 5, 0 (20) )…”

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confidence: 99%

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Inference on Weibull parameters under a balanced two‐sample type II progressive censoring scheme

Mondal

Kundu

2019

Quality & Reliability Eng

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The progressive censoring scheme has received a considerable amount of attention in the last 15 years. During the last few years, joint progressive censoring scheme has gained some popularity. Recently, the authors Mondal and Kundu ("A New Two Sample Type-II Progressive Censoring Scheme," Communications in Statistics-Theory and Methods) introduced a balanced two-sample type II progressive censoring scheme and provided the exact inference when the two populations are exponentially distributed. In this article, we consider the case when the two populations follow Weibull distributions with the common shape parameter and different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters. It is observed that the maximum likelihood estimators cannot be obtained in explicit forms; hence, we propose approximate maximum likelihood estimators, which can be obtained in explicit forms. We construct the asymptotic and bootstrap confidence intervals of the population parameters. Further, we derive an exact joint confidence region of the unknown parameters. We propose an objective function based on the expected volume of this confidence region, and using that, we obtain the optimum progressive censoring scheme. Extensive simulations have been performed to see the performances of the proposed method, and one real data set has been analyzed for illustrative purposes. KEYWORDS approximate maximum likelihood estimator, joint confidence region, joint progressive censoring, maximum likelihood estimator, optimum censoring scheme, progressive censoring, type II censoring MSC CLASSIFICATION 62N01; 62N02; 62F10 Qual Reliab Engng Int. 2020;36:1-17.wileyonlinelibrary.com/journal/qre

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Inference and optimal censoring schemes for progressively censored Birnbaum–Saunders distribution

Cited by 67 publications

References 28 publications

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

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

Inference on Weibull parameters under a balanced two‐sample type II progressive censoring scheme

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

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