Let Rn be the range of a random sample X1,...,Xn of exponential random variables with hazard rate [lambda]. Let Sn be the range of another collection Y1,...,Yn of mutually independent exponential random variables with hazard rates [lambda]1,...,[lambda]n whose average is [lambda]. Finally, let r...

In this paper, we introduce a new copula-based dependence order to compare the relative degree of dependence between two pairs of random variables. Relationship of the new order to the existing dependence orders is investigated. In particular, the new ordering is stronger than the partial...

A sufficient condition for comparing convolutions of heterogeneous exponential random variables in terms of right spread order is established. As a consequence, it is shown that a convolution of heterogeneous independent exponential random variables is more skewed than that of homogeneous...

In this paper, the sample range from a heterogeneous exponential sample is shown to be larger than that from a homogeneous exponential sample in the sense of the star ordering. Then, by using this result, some equivalent characterizations of stochastic comparisons of sample ranges with respect...

This paper studies capital allocation problems using a general loss function. Stochastic comparisons are conducted for general loss functions in several scenarios: independent and identically distributed risks; independent but non-identically distributed risks; comonotonic risks. Applications in...

This paper studies capital allocation problems with the aggregate risk exceeding a certain threshold. We propose a novel capital allocation rule based on the Tail Mean–Variance principle. General formulas for the optimal capital allocations are proposed. Explicit formulas for optimal capital...