Distributions of Quadratic Forms
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, Dawson's 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 24, 1987
- Accession Number
- ADA190224
Entities
People
- Herbert Solomon
- Mary E. Bock
Organizations
- Stanford University