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New Explicit Examples of Fixed Points of Poisson Shot Noise Transforms
Author(s) -
Iksanov Aleksander M.,
Kim Che Soong
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00332.x
Subject(s) - mathematics , shot noise , poisson distribution , convexity , uniqueness , fixed point , mathematical analysis , noise (video) , pure mathematics , statistics , image (mathematics) , computer science , telecommunications , artificial intelligence , detector , financial economics , economics
Summary The main objective of this paper is to establish a close relation between the fixed points of Poisson shot noise transforms and perpetuities of a special type. With this relation it is shown that the gamma distributions, the generalized positive Linnik distributions, and the S2 distributions are fixed points of Poisson shot noise transforms. The paper also proves that log‐convexity of the response functions is not needed for non‐negative Poisson shot noise distributions to be self‐decomposable. Finally, the problems of existence and uniqueness of the above mentioned perpetuities are investigated.