On the Distribution of the Sum ofNSample Values Drawn from a Truncated Normal Population

Abstract

This paper deals with the situation arising when a normal population has all members with values greater (or less) than a given value rejected, and where small samples are drawn from the remaining truncated population. Formal expressions are deduced from which can be calculated the distribution of the sum (or mean) of the sample values as a function of the point at which the original parent population is cut. Tables are given for the integral distribution function of the sum, standardised in an appropriate fashion, and their importance in solving a type of problem of quite frequent occurrence is shown.