On an Extension of Min-Semistable Distributions

Mohamed Ben Alaya; Thierry Huillet; Anna Porzio

hal-00136135, version 1

On an Extension of Min-Semistable Distributions

Mohamed Ben Alaya ¹, Thierry Huillet () ², Anna Porzio ^1, 3

Probability and Mathematical Statistics 27, No 2 (2007) 303-323

Abstract: 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 function can be identified by their behavior at the origin. Our constructed solutions are in this subclass. The uniqueness question is also discussed.

1: Laboratoire Analyse, Géométrie et Application (LAGA)
CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis
2: Laboratoire de Physique Théorique et Modélisation (LPTM)
CNRS : UMR8089 – Université de Cergy Pontoise
3: Centre de Physique Théorique (CPHT)
CNRS : UMR7644 – Polytechnique - X

hal-00136135, version 1
http://hal.archives-ouvertes.fr/hal-00136135
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From: Thierry Huillet <>
Submitted on: Monday, 12 March 2007 15:21:56
Updated on: Monday, 10 December 2007 15:57:19

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