The proportional likelihood ratio order and applications

  1. Ramos Romero, Héctor Manuel
  2. Sordo Díaz, Miguel Angel
Journal:
Questiió: Quaderns d'Estadística, Sistemes, Informatica i Investigació Operativa

ISSN: 0210-8054

Year of publication: 2001

Volume: 25

Issue: 2

Pages: 211-223

Type: Article

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Abstract

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). As an application, we show that the IPLR and DPLR properties are sufficient conditions for the Lorenz ordering of truncated distributions

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