Inference for a Simple Step-Stress Model with Type-I Censoring and Lognormally Distributed Lifetimes

Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows the experimenter to obtain failure data more quickly at increased stress levels than under normal operating conditions. A step-stress model is one special class of ALT, and in this article we consider a simple step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-I censoring. We then discuss inferential methods for the unknown parameters of the model by the maximum likelihood estimation method. Some numerical methods, such as the Newton–Raphson and quasi-Newton methods, are discussed for solving the corresponding non-linear likelihood equations. Next, we discuss the construction of confidence intervals for the unknown parameters based on (i) the asymptotic normality of the maximum likelihood estimators (MLEs), and (ii) parametric bootstrap resampling technique. A Monte Carlo simulation study is carried out to examine the performance of these methods of inference. Finally, a numerical example is presented in order to illustrate all the methods of inference developed here.     

Minimum and Maximum Information Censoring Plans in Progressive Censoring

Expressions for the entropy, the Kullback-Leibler information, and the I _α-information are established for distributions of progressively Type-II censored order statistics. These results are used to identify minimum and maximum information censoring plans. In particular, we find minimum and maximum entropy plans for DFR, exponential, Pareto, reflected power, and Weibull distributions. The results for Kullback-Leibler and I _α-information hold for any continuous distribution.     

Semiparametric Regression Analysis of Panel Count Data with Time-Dependent Covariates and Informative Observation and Censoring Times

In this article, we extend the joint frailty models proposed by Zhao and Tong (2011 Zhao , X. , Tong , X. ( 2011 ). Semiparametric regression analysis of panel count data with informative observation times . Comput. Statist. Data. Anal. 55 : 291 – 300 .[Crossref], [Web of Science ®] , [Google Scholar]) to panel count data with the time-dependent covariates and informative observation and censoring times. A novel estimating equation approach that does not depend on the distribution of frailty variables and the link function is proposed for estimation of parameters, and the asymptotic properties of the proposed estimators are established. Simulation studies demonstrate that the proposed inference procedure performs well. The analysis of a bladder tumor data is presented to illustrate the method.     

Interval Estimation of the Stress-Strength Reliability with Independent Normal Random Variables

This article develops a procedure to obtain highly accurate confidence interval estimates for the stress-strength reliability R = P(X > Y) where X and Y are data from independent normal distributions of unknown means and variances. Our method is based on third-order likelihood analysis and is compared to the conventional first-order likelihood ratio procedure as well as the approximate methods of Reiser and Guttman (1986 Reiser, B., Guttman, I. (1986). Statistical inference for Pr(Y < X): the normal case. Technometrics 28: 253257.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Guo and Krishnamoorthy (2004 Guo, H., Krishnamoorthy, K. (2004). New approximate inferential methods for the reliability parameter in a stress-strength model: the normal case. Commun. Statist. Theor. Meth. 33: 17151731.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The use of our proposed method is illustrated by an empirical example and its superior accuracy in terms of coverage probability and error rate are examined through Monte Carlo simulation studies.     

Gamma shared frailty model based on reversed hazard rate

Abstract

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor(frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set.     

Maximum likelihood estimation,from doubly censored samples,of the mean of a normal distribution with known coeffucient of variation

Let x be a random variable having the normal distribution with mean μ and variance c²μ², where c is a known constant. The maximum likelihood estimation of μ when the lowest r₁ and the highest r₂ sample values censored have been given the asymptotic variance of the maximum likelihood estimator is obtained.     

Testing a censoring hypothesis through an identity test

Given two samples drawn from the same, unknown, population, it is assumed to be known that only one has possibly been censored and which one it is. A nonparametric procedure to test the no censoring null hypothesis against the alternative censoring hypothesis is discussed.