Analysis of middle-censored data with exponential lifetime distributions

Abstract

Recently Jammalamadaka and Mangalam [2003. Non-parametric estimation for middle censored data. J. Nonparametric Statist. 15, 253--265] introduced a general censoring scheme called the "middle-censoring'' scheme in non-parametric set up. In this paper we consider this middlecensoring scheme when the lifetime distribution of the items is exponentially distributed and the censoring mechanism is independent and non-informative. In this set up, we derive the maximum likelihood estimator and study its consistency and asymptotic normality properties. We also derive the Bayes estimate of the exponential parameter under a gamma prior. Since a theoretical construction of the credible interval becomes quite difficult, we propose and implement Gibbs sampling technique to construct the credible intervals. Monte Carlo simulations are performed to evaluate the small sample behavior of the techniques proposed. A real data set is analyzed to illustrate the practical application of the proposed methods.

Analysis of discrete lifetime data under middle-censoring and in the presence of covariates

“…In this section, first we show how one can utilize the connection between the geometric and exponential distributions so that the results in DP can be subsumed by what has been done in [6] for exponential data. This connection will also allow us to more readily extend the results to the case of covariates, as we do in Section 2.2.…”

“…Jammalamadaka and Iyer [8], then suggested an approximate self-consistent estimator and established its weak convergence. Iyer et al [6] considered middle-censoring scheme in a parametric set-up when the lifetime distributions are exponentially distributed. They consider maximum likelihood and Bayes estimates of the relevant parameters.…”

“…In Section 2.1, we discuss this connection and use it in Section 2.2 to find the maximum likelihood estimates (MLEs) under middle-censoring in the presence of covariates using the accelerated failure time model for the geometric case and discuss the EM algorithm for obtaining them. The novelty of our approach, contrasted with that in DP [3], is to adapt the methods of Iyer et al [6] to the geometric case. Simulation studies are carried out in support of the theory to indicate how well the proposed estimation methods work.…”

“…In this paper, we consider discrete lifetime data that follow a geometric distribution that is subject to middle censoring. Two major innovations in this paper, compared to the earlier work of Davarzani and Parsian [3], include (i) an extension and generalization to the case where covariates are present along with the data and (ii) an alternate approach and proofs which exploit the simple relationship between the geometric and the exponential distributions, so that the theory is more in line with the work of Iyer et al [6]. It is also demonstrated that this kind of discretization of life times gives results that are close to the original data involving exponential life times.…”

A general censoring scheme for circular data

“…We consider both parametric and nonparametric estimation problems in this context and evaluate the loss in efficiency because of such censoring. See for instance, Iyer et al [1] who consider censoring in an exponential model.…”