Displaying similar documents to “Strong result for real zeros of random algebraic polynomials.”

The proportional likelihood ratio order and applications.

Héctor M. Ramos Romero, Miguel Angel Sordo Díaz (2001)

Qüestiió

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In this paper, we introduce a new stochastic order between continuous non-negative random variables called the PLR (proportional likelihood ratio) order, which is closely related to the usual likelihood ratio order. The PLR order can be used to characterize random variables whose logarithms have log-concave (log-convex) densities. Many income random variables satisfy this property and they are said to have the IPLR (increasing proportional likelihood ratio) property (DPLR property)....

Preservation of log-concavity on summation

Oliver Johnson, Christina Goldschmidt (2006)

ESAIM: Probability and Statistics

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We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. We introduce conditions under which the result still holds for dependent variables. We argue that these conditions are natural by giving some applications. Firstly, we use our main theorem to give simple proofs of the log-concavity of the Stirling numbers of the second kind and of the Eulerian numbers. Secondly, we prove results concerning the log-concavity of...