Associated Random Variables and Related Concepts

Abstract

In classical statistical inference, the observed random variables of interest are generally assumed to be independent and identically distributed. However in some real life situations, the random variables need not be independent. In reliability studies, there are structures in which the components share the load, so that failure of one component results in increased load on each of the remaining components. Minimal path structures of a coherent system having components in common behave in a ‘similar’ manner. Failure of a component will adversely effect the performance of all the minimal path structures containing it. In both the examples given above, the random variables of interest are not independent but are “associated” , a concept we will define soon. This book is concerned with the study of properties of stochastic processes termed as demimartingales and N-demimartingales and related concepts. As we will see in the next chapter, an important example of a demimartingale is the sequence of partial sums of mean zero associated random variables. We will now briey review some properties of associated random variables. We will come back to the study of these sequences again in Chapter 6.