Interval Dependence Structures of Two Bivariate Distributions in Risk and Reliability

We follow the ideas of measuring strength of dependence between random events, presented at two previous MMR conferences in South Africa and Tokyo. In our work here we apply it for analyzing local dependence structure of some popular bivariate distributions. At the Grenoble conference presentation we focus on the Bivariate Normal distributions with various correlation coefficients, and on the Marshal-Olkin distribution with various parameter’s combinations. We draw the surface z = gii(x,y), i=1,2 of dependence of i-th component on the other component j≠i within the squares [x, x +1]x[y,y+1], and [x, x +.5]x[y,y+.5]. The points (x,y) run within the square [-3.5, 3.5]x[-3.5, 3.5] for Bivariate Normal distribution, and in [0.10]x[0,10] for the Marshal-Olkin distribution.