A Characterization Related to the Equilibrium Distribution Associated with a Polynomial Structure
2010 ◽
Vol 47
(01)
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pp. 293-299
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Keyword(s):
Let f be a probability density function on (a, b) ⊂ (0, ∞), and consider the class C f of all probability density functions of the form Pf, where P is a polynomial. Assume that if X has its density in C f then the equilibrium probability density x ↦ P(X > x) / E(X) also belongs to C f : this happens, for instance, when f(x) = Ce−λx or f(x) = C(b − x)λ−1. We show in the present paper that these two cases are the only possibilities. This surprising result is achieved with an unusual tool in renewal theory, by using ideals of polynomials.
1998 ◽
Vol 39
(3)
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pp. 350-354
2021 ◽
pp. 40-52
1965 ◽
Vol 2
(02)
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pp. 286-292
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2013 ◽
Vol 46
(1)
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pp. 88-92
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2017 ◽
Vol 17
(6)
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pp. 1473-1490
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2007 ◽
Vol 40
(2)
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pp. 371-375
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