# Accession Number:

## AD0420434

# Title:

## THE DOUBLY NON-CENTRAL F-DISTRIBUTION EXPRESSED IN FINITE TERMS,

# Descriptive Note:

# Corporate Author:

## MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB

# Personal Author(s):

# Report Date:

## 1963-09-13

# Pagination or Media Count:

## 56.0

# Abstract:

There is an attempt to provide new, explicit and exact formulas for the doubly non-central F-distribution, defined as the cumulative distribution function, where the numbers of degrees of freedom of the chi-square variates need not be equal, but are restricted to be either both even or both odd. The formula for the even-even case is considerably simpler in structure than that for the odd-odd case, although the former involves Bessel functions where the latter contains error-functions. Therefore, at least for high degree-numbers it may be more convenient to try interpolation between the degree-numbers on numerical results obtained from the even-even formula when dealing with odd-odd cases, than to use the odd-odd formula directly. Mixed cases, where one degree-number is even and the other is odd, do not at present appear susceptible of analysis, so that here interpolation offers the only hope short of literal numerical integration. Author