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

Abstract

The two most popular censoring schemes are type-I and type-II censoring schemes. Hybrid censoring scheme is a mixture of type-I and type-II censoring schemes. In this paper we mainly consider the analysis of hybrid censored data when the lifetime distribution of the individual item is a two-parameter generalized exponential distribution. It is observed that the maximum likelihood estimators can not be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators. We obtain the observed Fisher information matrix using the missing information principle and it can be used for constructing the asymptomatic confidence intervals. We also obtain the Bayes estimates of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. One data set has been analyzed for illustrative purposes.

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

“…We can some numerical method to solve (7) and (8) Escobar [17] reported that the confidence interval in based on the asymptotic theory of ) ln(λ is superior to that of λˆ. α .…”

“…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] .…”

Statistical inference for the burr type III distribution under type II censored data

“…Thus,ĉ = c (h+1) andk = k (h+1) for which h is the smallest integer such that the convergence criterion holds. The maximization procedure can be done as given by Kundu and Pradhan [23]. First, c (h+1) is obtained by solving the …xed point type equation…”

Bayesian Prediction under a Finite Mixture of Generalized Exponential Lifetime Model

“…Extensive work has been done by several authors on GE( ) distribution. Some of the recent references on GE( ) distribution are (Gupta & Kundu, 2001), (Gupta & Kundu, 2002), (Jaheen, 2004), (Raqab & Madi, 2005), (Kundu, et al, 2005), (Gupta & Kundu, 2007), (Kundu & Gupta, 2008), (Kundu & Pardhan, 2008) and (Kim & Song, 2010). …”