Weak Stochastic Dependence " and Semi-Pseudonormal Probability Ditributions (original) (raw)

2010

Abstract

We investigate quantified (continuous) relationships between life time T of a technical or biological objects and stresses X1, … , Xm the objects endure. The basic distinction is recognized between an algebraic transformations of random stresses into the random life time, say, (X1, … , Xm) --> T and the weak transformations. The latter are understood as the transformations of the same stresses into the probability distribution F(t; theta) of T, where theta is a scalar or vector parameter of the distribution F. The weak transformation: (X1, … , Xm) --> F(t; theta) is defined as transformation of stresses realizations (x1, … , xm) --> theta (into the parameter(s) of F) so that an “old” (baseline) value of the parameter(s) theta turns into a new value theta(x1, … , xm). In such a way the baseline distribution F(t; theta) turns into the conditional one F(t | x1, … , xm) = F(t; theta(x1, … , xm) ). If the joint probability distribution of the random vector (X1, … , Xm) is known then the way for construction of new m+1 dimensional probability distributions is open with a variety of applications. Examples of such applications are provided.

Lidia Filus hasn't uploaded this paper.

Let Lidia know you want this paper to be uploaded.

Ask for this paper to be uploaded.