‎Independent random‎ ‎variables $Y_{1},ldots‎ ,‎Y_{n}$ belongs to the‎ ‎proportional reversed hazard rate (PRHR) model with‎ ‎proportionality parameters $lambda_1,...,lambda_n$‎, ‎if‎ ‎$Y_{k}sim G^{lambda _{k}}(x)$‎, ‎for $k=1,...,n$‎, ‎where $G$ is an‎ ‎absolutely continuous distribution function‎. ‎In this paper we compare‎ ‎the smallest order‎ ‎statistics‎, ‎the sample ranges and th...

In this paper, existence, uniqueness and continuity of the adapted solutions for neutral stochastic delay Volterra equations with singular kernels are discussed. In addition, continuous dependence on the initial date is also investigated. Finally, stochastic Volterra equation with the kernel of fractional Brownian motion is studied to illustrate the effectiveness of our results.

A general portfolio of joint life insurance contracts is studied in a stochastic interest rate environment with independent and dependent mortality models. Two types of joint insurance products, namely joint first-to-die and joint last-to-die, are considered in this project. Two methods are used to derive the first two moments of the prospective loss random variable. The first one is based on t...

A conditional spatial autoregression (CAR) specifies dependence via a weight matrix. Employing a doubly stochastic weight matrix allows users to interpret the CAR prediction rule as a semiparametric prediction rule and as BLUP with smoothing in addition to other benefits. We examine standard and doubly stochastic weight matrices in the context of an illustrative data set to demonstrate feasibil...