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...

Intuitively, activating the standby of a k-out-of-n:G system to the working state at the last moment fully utilizes the redundancy and hence would result in a more reliable system; however, this is not always true as shown in a counterexample. This paper presents several scenarios under which,...

The Lp-metric Δh,p(X) between the survival function F¯ of a random variable X and its distortion h∘F¯ is a characteristic of the variability of X. In this paper, it is shown that if a random variable X is larger than another random variable Y in the location-independent risk order or in the...

We explore the statistical behavior of the order statistics of the flights of one-sided Lévy processes (OLPs). We begin with the study of the extreme flights of general OLPs, and then focus on the class of selfsimilar processes, investigating the following issues: (i) the inner hierarchy of the...

Let ηt be a Poisson point process of intensity t≥1 on some state space Y and let f be a non-negative symmetric function on Yk for some k≥1. Applying f to all k-tuples of distinct points of ηt generates a point process ξt on the positive real half-axis. The scaling limit of ξt as t tends...

Let m be a random tessellation in Rd, d≥1, observed in a bounded Borel subset W and f(⋅) be a measurable function defined on the set of convex bodies. A point z(C), called the nucleus of C, is associated with each cell C of m. Applying f(⋅) to all the cells of m, we investigate the order...