APPROXIMATIONS TO NON-CENTRAL X² AND F DISTRIBUTIONS

抄録

Recently, a new higher order approximation to a percentage point for a non-central t-distribution was proposed by Akahira [1] using the Cornish-Fisher expansion and was shown to be better than prior approximations. In this paper approximation formulae for percentage points of the non-central x² and F distribution are proposed in a similar way to the above. An approximation formula of a percentage point of the non-central x² distribution is also given by a direct application of the Cornish-Fisher expansion for the chi-square statistic. Further, the numerical comparison of these formulae with former formulae shows that the new approximation formulae behave better than the others.