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

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

Onderzoeksoutput: Boek/rapportRapportAcademic

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Samenvatting

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.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijEurandom
Aantal pagina's10
StatusGepubliceerd - 2009

Publicatie series

NaamReport Eurandom
Volume2009025
ISSN van geprinte versie1389-2355

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