Motivated by marine ecological data on species abundance, with the record of subsamples, two problems are investigated in this paper, assuming the Ewens–Pitman sampling formula: One is the prediction of the number of new species if the catch is continued, and the other is how the number of...

An integral representation is derived for the sum of all claims over a finite interval when the claim value depends upon its incurral time. These time dependent claims, which generalize the usual compound model for aggregate claims, have insurance applications involving models for inflation and...

Let {Xi, i[greater-or-equal, slanted]1} be a sequence of i.i.d. random vectors inRd, and let[nu]p, 0p1, be a positive, integer valued random variable, independent ofXis. The[nu]-stable distributions are the weak limits of properly normalized random sums [summation...