Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme

Cho, Youngseuk; Sun, Hokeun; Lee, Kyeong‐Jun

doi:10.1016/j.stamet.2014.09.002

Cited by 118 publications

(91 citation statements)

References 17 publications

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“…Some special cases using exponential and Weibull distributions are obtained, i.e., based on Type-I GPHCS, Cho et al [4] results were generalized in the case of exponential and Weibull distributions at 1 α θ = = and 1 θ = , respectively. Also, based on Type-II GPHCS, Lee et al [7] results in the case of exponential parameter can be obtained as a special case at 1 α θ = = as well as if putting 1 θ = , Ashour and Elshahhat [1] results can be obtained as a special case in the case of Weibull distribution.…”

Section: Discussionmentioning

confidence: 99%

“…Also, Cho et al [4] results can be obtained as a special case from (6), if putting 1 α θ = = , we get the MLE β in the case of exponential parameter β , if putting 1 θ = , we get the MLEs α and β in the case of Weibull parameters α and β , respectively.…”

Section: American Journal Of Applied Mathematics and Statisticsmentioning

confidence: 94%

“…Cho et al [4] obtained the exact distribution of the MLE as well as exact lower confidence bound for the exponential parameter under Type-I GPHCS. Lee et al [7] obtained the MLE for the unknown parameter of exponential distribution under Type-II GPHCS.…”

Section: Introductionmentioning

confidence: 99%

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Parameters Estimation for the Exponentiated Weibull Distribution Based on Generalized Progressive Hybrid Censoring Schemes

Elshahhat¹

2017

AJAMS

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Based on Type-I and Type-II generalized progressive hybrid censoring schemes, the maximum likelihood estimators and Bayes estimators for the unknown parameters of exponentiated Weibull lifetime model are derived. The approximate asymptotic variance-covariance matrix and approximate confidence intervals based on the asymptotic normality of the classical estimators are obtained. Independent non-informative types of priors are considered for the unknown parameters to develop the Bayes estimators and corresponding Bayes risks under a squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. Finally, one real data set is analyzed for illustrative purposes.

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Section: Discussionmentioning

confidence: 99%

Section: American Journal Of Applied Mathematics and Statisticsmentioning

confidence: 94%

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Parameters Estimation for the Exponentiated Weibull Distribution Based on Generalized Progressive Hybrid Censoring Schemes

Elshahhat¹

2017

AJAMS

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“…Assume that X 1 , X 2 , · · · , X n denote the corresponding lifetimes from a distribution with cdf F (x) and pdf f (x). A generalized progressive hybrid censoring scheme is described as follows (Cho et al [15]). The integer k, m ∈ {1, 2, · · · , n} is pre-fixed, such that k < m and also R 1 , R 2 , · · · , R m are pre-fixed integers satisfying m i=1 R i + m = n. T ∈ (0, ∞) is a pre-fixed time point.…”

Section: Generalized Progressive Hybrid Censoringmentioning

confidence: 99%

Estimating the Entropy of a Weibull Distribution under Generalized Progressive Hybrid Censoring

Cho

Sun

Lee

2015

Entropy

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Recently, progressive hybrid censoring schemes have become quite popular in a life-testing problem and reliability analysis. However, the limitation of the progressive hybrid censoring scheme is that it cannot be applied when few failures occur before time T . Therefore, a generalized progressive hybrid censoring scheme was introduced. In this paper, the estimation of the entropy of a two-parameter Weibull distribution based on the generalized progressively censored sample has been considered. The Bayes estimators for the entropy of the Weibull distribution based on the symmetric and asymmetric loss functions, such as the squared error, linex and general entropy loss functions, are provided. The Bayes estimators cannot be obtained explicitly, and Lindley's approximation is used to obtain the Bayes estimators. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, a real dataset has been analyzed for illustrative purposes.

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“…Refer to Balakrishnan & Kundub (2013) for a review about hybrid censoring, including progressive hybrid censoring. Cho et al (2015) proposed a generalized progressive hybrid censoring scheme for exponential distribution.…”

Section: Introductionmentioning

confidence: 99%

Parameters Estimation for Mixed Generalized Inverted Exponential Distributions with Type-II Progressive Hybrid Censoring

Tian¹,

Yang²,

Li³

et al. 2016

HJMS

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The type-II progressive hybrid censoring scheme, which is a mixture of type-II progressive and hybrid censoring schemes, has become substantially fashionable due to its flexibility of allowing for random removals of the remaining survival units at each failure time and terminating the experiment at a pre-specified time. In the literature, this censoring scheme has been used to analyze lifetime data for general population distributions such as exponential distributions and Weibull distributions. However, we seldom focus on parameter estimations for the mixture distribution, which is an important class of models in reliability analysis. This paper aims to investigate the estimation problem of mixed generalized inverted exponential distribution (MGIED) under the type-II progressive hybrid censoring scheme. The maximum likelihood estimators (MLEs) of the model are obtained via EM algorithm. Some simulations are implemented and a case of analysis is provided to illustrate the proposed method.

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Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme

Cited by 118 publications

References 17 publications

Parameters Estimation for the Exponentiated Weibull Distribution Based on Generalized Progressive Hybrid Censoring Schemes

Parameters Estimation for the Exponentiated Weibull Distribution Based on Generalized Progressive Hybrid Censoring Schemes

Estimating the Entropy of a Weibull Distribution under Generalized Progressive Hybrid Censoring

Parameters Estimation for Mixed Generalized Inverted Exponential Distributions with Type-II Progressive Hybrid Censoring

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