Explicit Form of the Distribution of the Behrens-Fisher D-Statistic

Summary The distribution of the Berhens-Fisher d-statistic is given explicit form for all combinations of (v 1 v 2) the degrees of freedom whether odd or even, or one odd and one even. The density function of the d-statistic is expressed in terms of an Appell function which lends itself to easy computation of tail-probabilities. Values of 97.5 and 95 per cent points of the distribution are tabulated for chosen values of (v 1, v 2).