With the assumption of Archimedean copula for the occurrence frequencies of the risks covered by an insurance policy, this note further investigates the allocation problem of upper limits and deductibles addressed in Hua and Cheung (2008a). Sufficient conditions for a risk averse policyholder to...

We study here extremes of residuals of the bivariate lifetime and the residual of extremes of the two lifetimes. In the case of generalized Marshall–Olkin model and the total time transformed exponential model, we first present some sufficient conditions for the extremes of residuals to be...

NBUC class life distributions are dealt with in this paper. Firstly, a lower bound of the reliability function based upon mean and variance (both assumed finite) is presented. It is shown that the bound effectively improves "known bounds" for NBU life distributions. Secondly, a sufficient...

Let X be a nonnegative random variable with mean [mu][less-than-or-equals, slant][infinity], and let TX be the total time on test transform of X. It has been observed in the literature that the inverse of TX is a distribution function with support (0,[mu]). In this paper, we identify the random...

Let X1,...,Xn be independent exponential random variables with respective hazard rates [lambda]1,...,[lambda]n, and let Y1,...,Yn be independent exponential random variables with common hazard rate [lambda]. This paper proves that X2:n, the second order statistic of X1,...,Xn, is larger than...

This paper studies the tail behavior of the Poisson shot-noise processes with interdependent and heavy-tailed random shocks. In the presence of statistical dependence between the shock and its arrival time we establish the asymptotic behavior of the tail probability. Two examples are presented...

This paper studies the multivariate mixed proportional reversed hazard rate model having dependent mixing variables. Stochastic comparison as well as aging properties in this model are investigated, and stochastic monotone properties of the population vector with respect to the mixing vector are...

This paper deals with the reversed hazard rate of general mixture models. Dependence and monotone properties of the reversed hazard rate are studied. Some lower bounds of the expected inactivity time of the overall population are presented with an application. Finally, preservation of DRHR under...

This note studies the allocation of an active redundant component in a series system. We mainly conduct a stochastic comparison between random lives of a series system with two components under two allocation choices. The case with a standby redundancy and when the system is parallel are...