Cornish–Fisher expansions about the F-distribution

摘要

Cornish and Fisher (1937) [1] gave a fourth order approximation for the percentile of the F-distribution by approximating the cumulants of Z=1/2logF. We obtain an alternative formula by approximating the cumulants of F.Hill and Davis (1968) [2] gave Cornish–Fisher type expansions about any asymptotically normal distribution. We specialize their results to give expansions about the F-distribution.