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On an extension of min-semistable distributions

100%

Ben Alaya M. , Huillet T. , Porzio A.

Probability and Mathematical Statistics

2007

tom Vol. 27, Fasc. 2

303--323

This work focuses on a functional equation which extends the notion of min-semistable distributions. Our main results are an existence theorem and a characterization theorem for its solutions. The first establishes the existence of a class of solutions of this equation under a condition on the first zero on the positive axis of the associated structure function. The second shows that solutions belonging to a subclass of complementary distribution functions can be identified by their behavior at the origin. Our constructed solutions are in this subclass. The uniqueness question is also discussed.

Regularly log-periodic functions and some applications

75%

Kevei P.

Probability and Mathematical Statistics

2020

tom Vol. 40, Fasc. 1

159--182

We prove a Tauberian theorem for the Laplace-Stieltjes transform, a Karamata-type theorem, and a monotone density theorem in the framework of regularly log-periodic functions. We provide several applications of these results: for example, we prove that the tail of a nonnegative random variable is regularly log-periodic if and only if the same holds for its Laplace transform at 0, and we determine the exact tail behavior of fixed points of certain smoothing transforms.