A characterization related to the equilibrium distribution associated with a polynomial structure

S.K. Bar-Lev, O.J. Boxma, G. Letac

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Abstract

Let f be a probability density function on (a, b) C (0, infinity) and consider the class Cf of all probability density functions of the form Pf where P is a polynomial. Assume that if X has its density in Cf then the equilibrium probability density x -> P(X > x)/E(X) also belongs to Cf : this happens for instance when f(x) = Ce-¿x or f(x) = C(b-x) ¿-1. The present paper shows that actually they are the only possible two cases. This surprising result is achieved with an unusual tool in renewal theory, by using ideals of polynomials.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages10
Publication statusPublished - 2009

Publication series

NameReport Eurandom
Volume2009025
ISSN (Print)1389-2355

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    Bar-Lev, S. K., Boxma, O. J., & Letac, G. (2009). A characterization related to the equilibrium distribution associated with a polynomial structure. (Report Eurandom; Vol. 2009025). Eurandom.