The Distribution of a Truncated Linear Difference between Independent Chi-Square Variates.

摘要

A comprehensive account is given of the properties of the distribution of a doubly-truncated linear difference between two independent chi-square variates. Expressions for the probability density function,distribution function,moments,moment generating function,and characteristic function of the distribution are obtained,primarily by making use of known results on hypergeometric functions. Emphasis is placed on representations thought to be useful for computations. In general,simple expressions are possible only when at least one of the chi-squares has an even number of detrees of freedom. The results should prove useful in studying the properties of truncated quadratic estimators of variance components. (Author)