(Elsevier, 2015) Berg, Christian; López García, José Luis; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
We revisit the product convolution semigroup of probability densities ec(t); c >
0 on the positive half-line with moments (n!)c and determine the asymptotic
behaviour of ec for large and small t > 0. This shows that (n!)c is indeterminate
as Stieltjes moment sequence if and only if c > 2. When c is a natural number
ec is a Meijer-G function. From the results about ec we obtain the asymptotic
behaviour at 1 of the convolution roots of the Gumbel distribution.