Ordering properties of sample minimum from Kumaraswamy-G random variables

Sample Spaces, Random Variables

1 Probabilities In talking about probabilities, the fundamental object is Ω, the sample space. Points (elements) in Ω are denoted (generically) by ω. We assign probabilities to subsets of Ω. Assume for the moment that Ω is finite or countably infinite. Thus Ω could be the space of all possible outcomes when a coin is tossed three times in a row or say, the set of positive integers. A probabilit...

Ordering Extremes of Interdependent Random Variables

For random variables with Archimedean copula or survival copula, we develop the reversed hazard rate order and the hazard rate order on sample extremes in the context of proportional reversed hazard models and proportional hazard models, respectively. The likelihood ratio order on sample maximum is also investigated for the proportional reversed hazard model. Several numerical examples are pres...

Multidimensional Stochastic Ordering and Associated Random Variables

On the minimum of several random variables

For a given sequence of real numbers a1, . . . , an we denote the k-th smallest one by k-min1≤i≤n ai. Let A be a class of random variables satisfying certain distribution conditions (the class contains N(0, 1) Gaussian random variables). We show that there exist two absolute positive constants c and C such that for every sequence of positive real numbers x1, . . . , xn and every k ≤ n one has c...

Ordered Random Variables from Discontinuous Distributions

In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither re...