Sums and Sums of squares of non-negative variables. Some distribution theory and an application

Economics

Further details

When the sample space is unrestricted the joint distribution of the sum and sum of squares of n random variates is fairly trivially obtained. But when the variates are restricted to be nonnegative it is far from trivial, and has not previously been obtained in closed form in the literature. The paper shows how to derive the density using a differential-geometric approach, and applies the result to the MLE's for the parameters in a censored normal model.