Biswabrata Pradhan

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

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 article, 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 cannot 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.

Parameter estimation of the hybrid censored log-normal distribution

The two most common censoring schemes used in life-testing experiments are Type-I and Type-II censoring schemes. The hybrid censoring scheme is mixture of Type-I and Type-II censoring schemes. In this work, we consider the estimation of parameters of log-normal distribution based on hybrid censored data. The parameters are estimated by the maximum likelihood method. It is observed that the maximum likelihood estimates cannot be obtained in a closed form. We obtain the maximum likelihood estimates of the unknown parameters using EM algorithm. We also propose approximate maximum likelihood estimates and these can be used as initial estimates for any iterative procedure. The Fisher information matrix has been obtained and it can be used for constructing asymptotic confidence intervals. The method of obtaining optimum censoring scheme is discussed. One data set is analysed for illustrative purposes.

Bayes estimation and prediction of the two-parameter gamma distribution

In this article, the Bayes estimates of two-parameter gamma distribution are considered. It is well known that the Bayes estimators of the two-parameter gamma distribution do not have compact form. In this paper, it is assumed that the scale parameter has a gamma prior and the shape parameter has any log-concave prior, and they are independently distributed. Under the above priors, we use Gibbs sampling technique to generate samples from the posterior density function. Based on the generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct HPD credible intervals. We also compute the approximate Bayes estimates using Lindleys approximation under the assumption of gamma priors of the shape parameter. Monte Carlo simulations are performed to compare the performances of the Bayes estimators with the classical estimators. One data analysis is performed for illustrative purposes. We further discuss the Bayesian prediction of future observation based on the observed sample and it is seen that the Gibbs sampling technique can be used quite effectively for estimating the posterior predictive density and also for constructing predictive intervals of the order statistics from the future sample.

Parametric Estimation of Quality Adjusted Lifetime (QAL) Distribution in Simple Illness-Death Model

We discuss parametric estimation of quality adjusted lifetime distribution in simple illness-death model. Model parameters are estimated by maximum likelihood method. The distribution of QAL is estimated by replacing the parameters by their estimates. A regression model is also considered. A simulation study investigates bias and precision of the estimate of QAL distribution and compares it with an existing nonparametric estimate. Another simulation study investigates the effect of model misspecification. Application of our methodology has been illustrated using the Stanford heart transplant data.

Computation of optimum reliability acceptance sampling plans in presence of hybrid censoring

The decision regarding acceptance or rejection of a lot of products may be considered through variables acceptance sampling plans based on suitable quality characteristics. A variables sampling plan to determine the acceptability of a lot of products based on the lifetime of the products is called reliability acceptance sampling plan (RASP). This work considers the determination of optimum RASP under cost constraint in the framework of hybrid censoring. Weibull lifetime models are considered for illustrations; however, the proposed methodology can be easily extended to any location-scale family of distributions. The proposed method is based on asymptotic results of the estimators of parameters of lifetime distribution. Hence, a Monte Carlo simulation study is conducted in order to show that the sampling plans meet the specified risks for finite sample size.

Analysis of hybrid censored competing risks data

In this paper, we consider the analysis of hybrid censored competing risks data, based on Coxs latent failure time model assumptions. It is assumed that lifetime distributions of latent causes of failure follow Weibull distribution with the same shape parameter, but different scale parameters. Maximum likelihood estimators (MLEs) of the unknown parameters can be obtained by solving a one-dimensional optimization problem, and we propose a fixed-point type algorithm to solve this optimization problem. Approximate MLEs have been proposed based on Taylor series expansion, and they have explicit expressions. Bayesian inference of the unknown parameters are obtained based on the assumption that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameters have Beta–Gamma priors. We propose to use Markov Chain Monte Carlo samples to compute Bayes estimates and also to construct highest posterior density credible intervals. Monte Carlo simulations are performed to investigate the performances of the different estimators, and two data sets have been analysed for illustrative purposes.

Bayes estimation for the Block and Basu bivariate and multivariate Weibull distributions

Block and Basu bivariate exponential distribution is one of the most popular absolute continuous bivariate distributions. Recently, Kundu and Gupta [A class of absolute continuous bivariate distributions. Statist Methodol. 2010;7:464–477] introduced Block and Basu bivariate Weibull (BBBW) distribution, which is a generalization of the Block and Basu bivariate exponential distribution, and provided the maximum likelihood estimators using EM algorithm. In this paper, we consider the Bayesian inference of the unknown parameters of the BBBW distribution. The Bayes estimators are obtained with respect to the squared error loss function, and the prior distributions allow for prior dependence among the unknown parameters. Prior independence also can be obtained as a special case. It is observed that the Bayes estimators of the unknown parameters cannot be obtained in explicit forms. We propose to use the importance sampling technique to compute the Bayes estimates and also to construct the associated highest posterior density credible intervals. The analysis of two data sets has been performed for illustrative purposes. The performances of the proposed estimators are quite satisfactory. Finally, we generalize the results for the multivariate case.

Parametric estimation of quality adjusted lifetime (QAL) distribution in progressive illness–death model

In this work, we consider the parametric estimation of quality adjusted lifetime (QAL) distribution in progressive illness-death models. The main idea of this paper is to derive the theoretical distribution of QAL for the progressive illness-death models, under parametric models for the sojourn time distributions in different states, and then replace the model parameters by their estimates obtained by standard techniques of survival analysis. The method of estimation of the model parameters is also described. A data set of IBCSG Trial V has been analyzed for illustration. Extension to more general illness-death models is also discussed.

Parametric Estimation of Quality Adjusted Lifetime (QAL) Distribution for two General Illness-Death Models

In this work, we consider the parametric estimation of quality adjusted lifetime (QAL) distribution for two general illness-death models, namely, competing illness-death model and reversible illness-death model. The first model is progressive and involves multiple states, while the second one incorporates possibility of recovery. The main focus of this paper is to derive the theoretical distribution of QAL for the two illness-death models, under some parametric models for the sojourn time distributions in different states. The QAL distribution is then estimated by replacing the parameters in its theoretical expression by the corresponding estimates obtained by using standard survival analysis techniques. The performance of the estimator is investigated through a simulation study. AMS (2000) Subject Classification : 62N02

Fisher information in generalized progressive hybrid-censored data

ABSTRACT This article provides a simple expression of the Fisher information matrix about the unknown parameter(s) of the underlying lifetime model under the generalized progressive hybrid censoring scheme. The expressions of the expected number of failures and the expected duration of life test are also derived. Exponential and Weibull lifetime models are considered for numerical illustrations. Finally, Fisher information-based optimal schemes are discussed for the Weibull lifetime model.