compound distributions of sum of single truncated random variables

Abstract

Since the early 1900's, the problem of the distribution of sums of random variables in probability theory has received a great deal of attention especially in case of two or three random variables. But generally in case of n random variables n systematic procedures for the distribution of sums of the form X; have been i=O

developed by some authors during 1930 40 .

The distribution of sums of truncated random variables in the form

n , where X; is a truncated random variable, have been treated by many i=O

researchers during years 19501975 when n is a constant number only, using the moment generating functions methods. Indeed, truncation is a general important property in real life problems such as industry of articles, especially in the theory of queues and reliability theory of electronic systems, in medicine as in hospital administration and many other fields.