Quantile estimation for a progressively censored exponential distribution

Abstract

In this paper, we consider the problem of estimating the quantile of a two-parameter exponential distribution with respect to an arbitrary strictly convex loss function under progressive type II censoring. Inadmissibility of the best affine equivariant (BAE) estimator is established through a conditional risk analysis. In particular we provide dominance results for quadratic, linex and absolute value loss functions. Further, a class of dominating estimators is derived using the IERD (integral expression of risk difference) approach of Kubokawa (1994 Kubokawa, T. 1994. A unified approach to improving equivariant estimators. The Annals of Statistics 22 (1):290–9. doi:10.1214/aos/1176325369.[Crossref], [Web of Science ®] , [Google Scholar]). In sequel the generalized Bayes estimator is shown to improve the BAE estimator.     

On progressively censored inverted exponentiated Rayleigh distribution

In this paper, we discuss a progressively censored inverted exponentiated Rayleigh distribution. Estimation of unknown parameters is considered under progressive censoring using maximum likelihood and Bayesian approaches. Bayes estimators of unknown parameters are derived with respect to different symmetric and asymmetric loss functions using gamma prior distributions. An importance sampling procedure is taken into consideration for deriving these estimates. Further highest posterior density intervals for unknown parameters are constructed and for comparison purposes bootstrap intervals are also obtained. Prediction of future observations is studied in one- and two-sample situations from classical and Bayesian viewpoint. We further establish optimum censoring schemes using Bayesian approach. Finally, we conduct a simulation study to compare the performance of proposed methods and analyse two real data sets for illustration purposes.     

Fisher information in generalized progressive hybrid-censored data

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.     

Estimation and prediction for Chen distribution with bathtub shape under progressive censoring

We consider estimation of the unknown parameters of Chen distribution [Chen Z. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statist Probab Lett. 2000;49:155–161] with bathtub shape using progressive-censored samples. We obtain maximum likelihood estimates by making use of an expectation–maximization algorithm. Different Bayes estimates are derived under squared error and balanced squared error loss functions. It is observed that the associated posterior distribution appears in an intractable form. So we have used an approximation method to compute these estimates. A Metropolis–Hasting algorithm is also proposed and some more approximate Bayes estimates are obtained. Asymptotic confidence interval is constructed using observed Fisher information matrix. Bootstrap intervals are proposed as well. Sample generated from MH algorithm are further used in the construction of HPD intervals. Finally, we have obtained prediction intervals and estimates for future observations in one- and two-sample situations. A numerical study is conducted to compare the performance of proposed methods using simulations. Finally, we analyse real data sets for illustration purposes.     

On estimating the reliability in a multicomponent stress-strength model based on Chen distribution

Abstract

In this article, we obtain point and interval estimates of multicomponent stress-strength reliability model of an s-out-of-j system using classical and Bayesian approaches by assuming both stress and strength variables follow a Chen distribution with a common shape parameter which may be known or unknown. The uniformly minimum variance unbiased estimator of reliability is obtained analytically when the common parameter is known. The behavior of proposed reliability estimates is studied using the estimated risks through Monte Carlo simulations and comments are obtained. Finally, a data set is analyzed for illustrative purposes.     

Estimation and prediction for an inverted exponentiated Rayleigh distribution under hybrid censoring

In this paper we consider estimation of unknown parameters of an inverted exponentiated Rayleigh distribution when it is known that data are hybrid Type I censored. The maximum likelihood and Bayes estimates are derived. In sequel interval estimates are also constructed. We further consider one- and two-sample prediction of future observations and also obtain prediction intervals. The performance of proposed methods of estimation and prediction is studied using simulations and an illustrative example is discussed in support of the suggested methods.