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The total time on test transform and the excess wealth stochastic orders of distributions

Part of: Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  01 July 2016

Subhash C. Kochar ,
Xiaohu Li  and
Moshe Shaked
Subhash C. Kochar*
Affiliation:
Indian Statistical Institute
Xiaohu Li*
Affiliation:
Lanzhou University
Moshe Shaked*
Affiliation:
University of Arizona
*
∗ Postal address: Stat-Math Unit, Indian Statistical Institute, 7 S.J.S. Sansanwal Marg, New Delhi 110016, India.
∗∗ Postal address: Department of Mathematics, Lanzhou University, Lanzhou 730000, People's Republic of China.
∗∗∗ Postal address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA. Email address: shaked@math.arizona.edu
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Abstract

For nonnegative random variables X and Y we write X ≤TTTY if ∫0F-1(p)(1-F(x))dx ≤ ∫0G-1(p)(1-G(x))dx all p ∈ (0,1), where F and G denote the distribution functions of X and Y respectively. The purpose of this article is to study some properties of this new stochastic order. New properties of the excess wealth (or right-spread) order, and of other related stochastic orders, are also obtained. Applications in the statistical theory of reliability and in economics are included.

Keywords

Excess wealth orderright-spread orderLorenz orderNBUEincreasing convex and concave ordersseries and parallel systemsHNBUEeconomic inequality measureempirical TTT transformtest for ‘more NBUE’

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 62N05: Reliability and life testing
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 4 , December 2002 , pp. 826 - 845
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Supported by NSFC under grants TY 10126014 and 10201010.

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