Exact likelihood inference for the exponential distribution under generalized Type‐I and Type‐II hybrid censoring

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

doi:10.1002/nav.20038

Cited by 124 publications

(72 citation statements)

References 5 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: 88%

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: 88%

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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“…Balakrishnan and Iliopoulos [3] formally proved that these conjectures are indeed true thus validating the exact inferential procedures developed by all these authors. Since then, more references about hybrid censoring can refer to Ebrahimi [4] ,Chandrasekhar, et al [5] ,Balakrishnan and Xie [6] ,Kundu et al [7] Balakrishnan et al [8] Cheng Conghua, Chen Jinyuan [9] .…”

Section: Introductionmentioning

confidence: 99%

Research of Data Model under Exponential Distribution Based on Type-II Hybrid Censored Sample

ZHANG¹,

Yu²,

LU³

2018

dtcse

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“…This HCS is called Type-II HCS. In the same respect, to avoid the disadvantages in these schemes, Chandrasekar et al [7] proposed two new schemes which are called generalized Type-I and Type-II HCS. In generalized Type-I HCS, fix k, r  (1, 2, …, n) and T  (0,∞) such that k < r < n. If the k th failure occurs before time T, the experiment is terminated at min {Xr:n; T}.…”

Section: Introductionmentioning

confidence: 99%

Exponentiated Rayleigh Distribution: A Bayes Study Using MCMC Approach Based on Unified Hybrid Censored Data

Mohamed¹

2017

JAM

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I S S N 2 3 4 7 -1 9 2 1 V o l u m e 1 2 N u m b e r 1 2 J o u r n a l o f A d v a n c e s i n M a t h e m a t i c s 6863 | P a g e J a n u a r y 2 0 1 7 w w w . hasaballahmohamed@yahoo.com ABSTRACT This paper aims to estimate the unknown parameters, survival and hazard functions for exponentiated Rayleigh distribution based on unified hybrid censored data. The maximum likelihood estimators (MLEs), Bayes, and parametric bootstrap methods are used for estimating the two unknown parameters as well as survival and hazard functions. We propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure. Approximate confidence intervals for the unknown parameters moreover survival and hazard functions are constructed based on the s-normal approximation to the asymptotic distribution of MLEs. The approximate Bayes estimators have been obtained under the assumptions of informative and non-informative priors depending on symmetric and asymmetric loss functions via the Gibbs within Metropolis-Hasting samplers procedure. Finally, the proposed methods can be understood through illustrating the results of the real data analysis.

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Exact likelihood inference for the exponential distribution under generalized Type‐I and Type‐II hybrid censoring

Cited by 124 publications

References 5 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

Research of Data Model under Exponential Distribution Based on Type-II Hybrid Censored Sample

Exponentiated Rayleigh Distribution: A Bayes Study Using MCMC Approach Based on Unified Hybrid Censored Data

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