2002/02/05 by Aleksander M. Iksanov, Iksanov, Aleksander M., Che Soong Kim +1
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #Probability and Risk Models #Statistical Distribution Estimation and Applications #math.PR #msc:60E07
paper · pdf · doi:10.48550/arxiv.math/0202035
12 pages
arxiv created 2002/09/02 · arxiv updated 2009/11/30
We show that gamma distributions, generalized positive Linnik distributions, S2 distributions are fixed points of Poisson shot noise transforms. The corresponding response functions are identified via their inverse functions except for some special cases when those can be obtained explicitly. As a by-product, it is proven that log-convexity of the response function is not necessary for selfdecomposability of non-negative Poisson shot noise distribution. Some attention is given to perpetuities of a rather special type which are closely related to our model. In particular, we study the problem of their existence and uniqueness.