We provide some characterization results of the first order statistic based on the generalized survival entropy and its dynamic version. We obtain characterization results of the generalized Pareto distribution. A generalization of the failure entropy of order α, namely generalized survival...

Estimation of the entropy of several exponential distributions is considered. A general inadmissibility result for the scale equivariant estimators is proved. The results are extended to the case of unequal sample sizes. Risk functions of proposed estimators are compared numerically.

The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, we show that the proportional hazard rates (PHR) model, which includes some well-known...

In this paper, we propose a new cure rate survival model, which extends the model of Rodrigues et al. (2011) by incorporating a structure of dependence between the initiated cells. To create the structure of the correlation between the initiated cells, we use an extension of the generalized...

Shmueli et al. (2005) introduced the COM–Poisson–binomial distribution, but they did not study the mathematical properties of this family of distributions. In this paper, we discuss some properties and an asymptotic approximation of it by the COM–Poisson distribution. Moreover, three...

We first compare the ranked set sampling (RSS) and simple random sampling schemes for the estimation of the population median through Pitman’s measure of closeness. Then, by using Banks’ criterion, we determine the frequency with which an individual order statistic is closer to the median...

In this paper, we establish some results for the increasing convex comparisons of generalized order statistics. First, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then the remaining generalized order statistics are also...

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...

Weibull mixtures have been used extensively in reliability and survival analysis, and they have also been generalized by allowing negative mixing weights, which arise naturally under the formation of some structures of reliability systems. These models provide flexible distributions for modeling...