Some novel discrete distributions under fourfold sampling schemes and conditional bivariate order statistics

This paper presents some novel trivariate discrete distributions that are obtained by modifying the bivariate binomial distribution. These distributions are important probability models for the development of conditional bivariate order statistics. The distributional properties of bivariate order statistics are studied and derived under the condition that certain values of the underlying random vectors (X,Y)(X,Y) are truncated and fall in the threshold set {(t,s)∈R2:t≤u,s≤v}{(t,s)∈R2:t≤u,s≤v}, (u,v)∈R2(u,v)∈R2.