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

Reliability Modeling of Political Processes

Probability offers some suitable tools for modeling political processes in a country\u27s life. It is well known that a party, or coalition can not govern a country without the support of more than 50 % of the voters, or the members of the National Assembly. However, the dynamics in political life is very similar to the k=out-of-n reliability systems for a political party. In the same time, a coalition is consisted by several parties (systems of similar type), and in order to govern must sustain more than 50 % of the governing entity. We explore Probabilistic ideas from queuing theory and reliability to create a reliability model for a political unit from different points of view: Existence (duration of life), governing survivability, life time distribution, longevity, resistance