New representations for the doubly noncentral f-distribution and derived distribution

Abstract

Representations of the doubly noncentral F-distribution are presented i n terms of the cdf of the noncentral chi-square. These are specialized t o the oncentral F and f o r an even number of degrees of freedom f o r the denominator the noncentral F is zxpressed as a weighted sum of noncentral t - probabilities When either or both of the degrees of freedom are even, this result is then specialized to give the F distribution in terms of Student's t - distribution

Keywords:

• Noncentral chi-squar
• Noncentral F
• F-distributio
• distribution; Noncentraz t-distri- bution
• Student's t-distributio