# Accession Number:

## ADA190224

# Title:

## Distributions of Quadratic Forms

# Descriptive Note:

## Technical rept.

# Corporate Author:

## STANFORD UNIV CA DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1987-11-24

# Pagination or Media Count:

## 17.0

# Abstract:

For independent chi-square variables x squared sub m and x squared sub n with m and n degrees of freedom, respectively, we consider the quadratic form where the positive ci are distinct. This paper gives exact finite expressions for the distribution of Q in terms of available functions such as the distribution function of chi-square random variables, modified Bessel Functions, Dawsons integral. These formulas are useful for checking the accuracy of approximations and tables of the distribution of Q and provide a simple alternative in their absence. For large m and n, reasonable approximations to the distribution of Q are available. For the general quadratic form Williams 1984 compares algorithms for truncations of infinite series expansions of the distribution.

# Descriptors:

# Subject Categories:

- Statistics and Probability