Moments of a Noncentral t and Noncentral F-distribution

A familiar textbook problemn is to determine the Imean of a noni-central F-variable (see Graybill, page 89). This had usually resulted in an unpleasant integration problein until the siimiple trick of inultiplying and dlividinig by the mean of an appropriate independent variable was considered. The moments of a noncentral t-distribution, non-central F-distribution, and possibly others, can be expressed in terins of inore familiar inoments by this method. The followviing notation will be used. Suppose X is normally distributed with mean a anl(l varianice 1, Z is normally distributed with imiean 0 andl variance 1, and that U. and VP are clii-square variables with q and p degrees of freedoin respectively. Also let f1 ,x = Z