A martingale-based test for independence of time to failure and cause of failure for competing risks models

In this article, we introduce a class of tests, using a martingale approach, for testing independence of failure time and cause of failure for competing risks data. Asymptotic distribution of the proposed test statistic is derived. The procedure is illustrated with a real-life data. A simulation study is carried out to assess the level and power of the test.     

江泽民关于科教兴国战略的新论述

江泽民高度重视科技与教育的关键作用和动力功能 ,对于科教兴国战略进行了深刻的理论阐发 ,为我们在新世纪坚持实施这一重大战略决策提供了重要的思想指导     

On tail-ordering and comparison of failure rates

In this paper, we have studied some implications between tail-ordering (also known as dispersive ordering) and failure rate ordering (also called TP₂ ordering) of two probability distribution functions. Based on independent random samples from these distributions, a class of distribution-free tests has been proposed for testing the null hypothesis that the two life distributions are identical against the alternative that one failure rate is uniformly smaller than the other. The tests have good efficiencies as compared to their competitors.     

Relations for reliability measures of weighted distributions

Relibility measures of weighted distribution of alifeistribution have been derived Sufficientconditions on the weight function have been obtained for the weighted distribution of an IFR distribution to be IFR. Length-biased and equilibrium distributions have been discussed as weighted distributions in the reliability context.     

An EM algorithm for the estimation of parameters of bivariate generalized exponential distribution under random left censoring

In this paper, we consider the four-parameter bivariate generalized exponential distribution proposed by Kundu and Gupta [Bivariate generalized exponential distribution, J. Multivariate Anal. 100 (2009), pp. 581–593] and propose an expectation–maximization algorithm to find the maximum-likelihood estimators of the four parameters under random left censoring. A numerical experiment is carried out to discuss the properties of the estimators obtained iteratively.     

Proportional hazards model for discrete data: Some new developments

ABSTRACT

Many times, a product lifetime can be described through a non negative integer valued random variable. In this article, we propose a proportional hazards model for discrete data analogous to the version for continuous data. Some ageing properties of the model are discussed. Stochastic comparison of pair of random variables that follow the model are also made. A new test based on U-statistics is developed for testing that the proportionality parameter in the proposed model is 1. The asymptotic properties of the proposed test are studied. We present some numerical results to asses the performance of the test procedure.     

A family of distributions to model load sharing systems

The main characteristic of a load sharing system is that after the failure of one component the surviving components have to shoulder extra load and hence are prone to failure at an earlier time than what is expected under the original model. In others, the failure of one component may release extra resources to the survivors, thus delaying the system failure. In this paper we consider such m component systems and some observation schemes and identifiability issues under them. Then we construct a general semiparametric multivariate family of distributions which explicitly models this phenomenon through proportional conditional hazards. We suggest estimates for the constant of proportionality. We propose a nonparametric test for the hypothesis that the failures take place independently according to the common distribution against the alternative hypothesis that the second failure takes place earlier than warranted, study its properties and illustrate its use.     

江泽民关于科教兴国战略的新论述

江泽民高度重视科技与教育的关键作用和动力功能 ,对于科教兴国战略进行了深刻的理论阐发 ,为我们在新世纪坚持实施这一重大战略决策提供了重要的思想指导     

Comparison of cumulative incidence functions of current status competing risks data with discrete observation times

Abstract

Competing risks data with current status censoring arise frequently from transversal studies in demography, epidemiology and reliability theory; where the only information about lifetime is whether the event of interest has occurred or not before a monitoring time. In practice, the monitoring times are discrete, but most of the studies consider them as continuous in nature. In the present paper, we propose a non parametric test for comparing cumulative incidence functions of current status competing risks data while the observation (monitoring) times are discrete. Asymptotic distribution of the test statistic is also derived. A simulation study is conducted to assess the finite sample behavior of the test statistic. The practical utility of the procedure is well demonstrated using a real-life data set on menopausal history of 2423 women given in Jewell, van der Laan, and Henneman (2003 Jewell, N. P., M. van der Laan, and T. Henneman. 2003. Nonparametric estimation from current status data with competing risks. Biometrika 90 (1):183–197. doi: 10.1093/biomet/90.1.183.[Crossref], [Web of Science ®] , [Google Scholar]).