Exact Likelihood Inference for an Exponential Parameter Under Progressive Hybrid Censoring Schemes

Childs, Aaron; Chandrasekar, B.; Balakrishnan, N.

doi:10.1007/978-0-8176-4619-6_23

Cited by 81 publications

(72 citation statements)

References 7 publications

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“…More specifically, for any u ∈ (0, 1), we have lim θ↑∞ F r ((n − 1 + u)T ; θ|D 1) = u when r > 1 and lim θ↑∞ F r (nuT ; θ|D 1) = u when r = 1 which means that the problem of nonexistence of a solution to the equation F r (y; θ|D 1) = u for particular values y is also present here. The same situation arises under type-I hybrid progressive censoring introduced by Childs et al (2008) (see also Cramer and Balakrishnan, 2013), generalized type-II hybrid censoring (Chandrasekar et al, 2004), progressive type-I censoring (Balakrishnan, 2007;Balakrishnan et al, 2011) and some other life-testing scenarios as well.…”

Section: Some Other Scenarios Facing the Same Problemmentioning

confidence: 87%

On the method of pivoting the CDF for exact confidence intervals with illustration for exponential mean under life-test with time constraints

Balakrishnan

Cramer

Iliopoulos

2014

Statistics & Probability Letters

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Two requirements for pivoting a cumulative distribution function (CDF) in order to construct exact confidence intervals or bounds for a real-valued parameter θ are the monotonicity of this CDF with respect to θ and the existence of solutions of some pertinent equations for θ. The second requirement is not fulfilled by the CDF of the maximum likelihood estimator of the exponential scale parameter when the data come from some life-testing scenarios such as type-I censoring, hybrid type-I censoring, and progressive type-I censoring that are subject to time constraints. However, the method has been used in these cases probably because the non-existence of the solution usually happens only with small probability. Here, we illustrate the problem by giving formal details in the case of type-I censoring and by providing some further examples. We also present a suitable extension of the basic pivoting method which is applicable in situations wherein the considered equations have no solution.

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Section: Some Other Scenarios Facing the Same Problemmentioning

confidence: 87%

On the method of pivoting the CDF for exact confidence intervals with illustration for exponential mean under life-test with time constraints

Balakrishnan

Cramer

Iliopoulos

2014

Statistics & Probability Letters

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“…. , X J:m:n } Let f (x) and F (x) denotes the probability density function and cumulative distribution func-tion of the distribution under study respectively then following Childs, Chandrasekar, and Balakrishnan (2008), we can write the likelihood function for the above mentioned two cases as follows:…”

Section: Model Description and Notationsmentioning

confidence: 99%

“…Keeping this point in mind, Kundu and Joarder (2006) proposed a new censoring scheme which is a mixture of hybrid and Type-II progressive censoring schemes and named it as Type-II progressive hybrid censoring which ensures that the experiment time can not exceed a prefixed time T ; see also Childs, Chandrasekar, and Balakrishnan (2008), Kundu (2007), Kundu, Joarder, and Krishna (2009)…”

Section: Introductionmentioning

confidence: 99%

Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

Chaturvedi

Singh

2018

AJS

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This article presents the procedures of parameter estimation based on Type-II progressively hybrid censored fuzzy lifetime data. Classical as well as the Bayesian procedures for the estimation of unknown model parameters has been developed. Keywords: Type-II progressive hybrid censoring, fuzzy lifetime data, Rayleigh distribution, maximum likelihood (ML) estimator, method of moments (MM) estimator, computational approach (CA) estimator.

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“…The disadvantages of the progressive Type-II censoring scheme are that the time of the experiment can be very long if the units are highly reliable. Therefore, Kundu and Joarder in [6] and Childs et al in [7] proposed a progressive Type-I hybrid censoring scheme (HCS), in this life-testing the experiment is terminated at time min{X m:m:n , T }, where T ∈ (0, ∞) pre-fixed in advance. Under progressive Type-I HCS, the time on experiment will be no more than T .…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference for Pareto Distribution based on Progressive Type-I Hybrid Censoring Scheme

El-Din¹,

Shafay²,

Nagy³

et al. 2017

IJCA

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In this paper, the maximum likelihood and Bayesian estimations are developed based on progressive Type-I hybrid censored sample from the Pareto distribution. The Bayesian estimators for the unknown parameters are computed using the squared error loss function. Also, the point and interval Bayesian predictions for the unobserved failures from the same sample and that from the future sample are derived. Moreover, a Monte Carlo simulation study is carried out to compare the performance of the maximum likelihood and the Bayesian estimators. Finally, numerical example is presented for illustrating all the inferential procedures developed here.

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Exact Likelihood Inference for an Exponential Parameter Under Progressive Hybrid Censoring Schemes

Cited by 81 publications

References 7 publications

On the method of pivoting the CDF for exact confidence intervals with illustration for exponential mean under life-test with time constraints

On the method of pivoting the CDF for exact confidence intervals with illustration for exponential mean under life-test with time constraints

Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

Statistical Inference for Pareto Distribution based on Progressive Type-I Hybrid Censoring Scheme

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