Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution

Abstract

Type-I and Type-II hybrid censoring, exponential distribution, order statistics, confidence bound, life testing,

Estimating the Parameters of the Generalized Exponential Distribution in Presence of Hybrid Censoring

“…In both the cases we have estimated the unknown parameters using the MLEs and the Bayes estimates. For computing the MLEs we have used the EM algorithm as described in Section 2 and also computed the 95% confidence intervals using the observed Fisher Finally we should mention that our method can be used for other censoring plans also, for example type-I, type-II, Type-II hybrid (see for example Childs et al [4] or progressive censoring plans. More work is needed in these directions.…”

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

“…This scheme was originally proposed by Epstein (1954) and was further studied by Chen and Bhattacharyya (1988) and Childs et al (2003); see also Balakrishnan and Kundu (2013). Chen and Bhattacharyya (1988) and Childs et al (2003) pivot the CDF (more specifically, the survival function) of the MLE of θ in order to obtain exact confidence bounds and intervals, respectively. The difference of this scheme from the standard type-I censoring is that the experiment terminates at the random time T * = min{X r:n , T }, where 1 r n. The idea is that in cases wherein the experimenter is satisfied with r observations, he/she is allowed to stop the experiment before the pre-determined time as soon as r failures have occured.…”

“…As in the case of conventional type-I censoring, this MLE is also defined if and only if D 1. Chen and Bhattacharyya (1988) gave an expression for the conditional CDF ofθ given D 1, which was further simplified by Childs et al (2003). Their expression of the CDF is…”

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

“…The failure times observed from such a life-test, 1: [10] discussed a Type-II hybrid censoring scheme in order to avoid the problem of having too few failures.in order to avoid the problem of having too few failures. Type-II hybrid censoring scheme in which the life testing experiment is terminated at a random time * [11] considered life testing situations where the lifetime follows the exponential distribution.…”