Motivated by the observation that for a sample of size two from an exponential distribution, the largest order statistic is distributed as a convolution of two independent exponential random variables with distributions differing only in their intensity or rate parameter, a spectrum of related...

We establish the uniform almost complete convergence, with rate, for estimators of both the cumulative hazard and the survival functions when the data are subject to twice censoring. Then, we derive similar convergence results for kernel type estimators of the density and the failure rate.

This paper aims to investigate the importance levels of the components in two groundwater remediation systems and examine the impact of each component on the whole system. Four measures are introduced including structural importance (SI), Birnbaum importance (BI), criticality importance (CI),...

Several univariate proportional reversed hazard models have been proposed in the literature. Recently, Kundu and Gupta (2010) proposed a class of bivariate models with proportional reversed hazard marginals. It is observed that the proposed bivariate proportional reversed hazard models have a...

Crevecoeur (1993) developed a three-parameter bathtub-shaped failure rate model that enjoys nice mathematical properties and justification from engineering perspectives. In this paper, we derive the explicit formulas for the maximum likelihood estimation (MLE) of parameters for his model applied...

In this paper, we further study the Conway–Maxwell Poisson distribution having one more parameter than the Poisson distribution and compare it with the Poisson distribution with respect to some stochastic orderings used in reliability theory. Likelihood ratio test and the score test are...

Within set-valued analysis there exist several notions related to the infinitesimal behavior of set-valued functions. One more such notion, needed for a class of spacial statistical problems, was proposed in Khmaladze (2007). Recently we found another suitable characteristic of this evolution,...