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A class of location-independent variability orders, with applications

Part of: Distribution theory - Probability Mathematical economics Applications

Published online by Cambridge University Press:  14 July 2016

Moshe Shaked ,
Miguel A. Sordo  and
Alfonso Suárez-Llorens
Moshe Shaked*
Affiliation:
University of Arizona
Miguel A. Sordo*
Affiliation:
Universidad de Cádiz
Alfonso Suárez-Llorens*
Affiliation:
Universidad de Cádiz
*
∗Postal address: Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA. Email address: shaked@math.arizona.edu
∗∗Postal address: Departamento de Estadística e I. O., Universidad de Cádiz, C/ Duque de Nájera 8, CP: 11002, Cádiz, Spain.
∗∗Postal address: Departamento de Estadística e I. O., Universidad de Cádiz, C/ Duque de Nájera 8, CP: 11002, Cádiz, Spain.
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Abstract

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Li and Shaked (2007) introduced the family of generalized total time on test transform (TTT) stochastic orders, which is parameterized by a real function h that can be used to capture the preferences of a decision maker. It is natural to look for properties of these orders when there is an uncertainty in determining the appropriate function h. In this paper we study these orders when h is nondecreasing. We note that all these orders are location independent, and we characterize the dispersive order, and the location-independent riskier order, by means of the generalized TTT orders with nondecreasing h. Further properties, which strengthen known properties of the dispersive order, are given. A useful nontrivial closure property of the generalized TTT orders with nondecreasing h is obtained. Applications in poverty comparisons, risk management, and reliability theory are described.

Keywords

Dispersive orderexcess wealth orderstochastic orderlocation-independent riskier orderincreasing convex and concave orderspoverty measurerisk comparisontaxation policyNBUIFR

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 62P20: Applications to economics 91B30: Risk theory, insurance
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 2 , June 2010 , pp. 407 - 425
Copyright
Copyright © Applied Probability Trust 2010 

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