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

Subhash C. Kochar; Xiaohu Li; Moshe Shaked

doi:10.1239/aap/1037990955

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

Subhash C. Kochar
, Xiaohu Li
, Moshe Shaked

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

74 Scopus citations

Abstract

For nonnegative random variables X and Y we write X ≤_TTT Y if ∫₀^F-1(p)(1-F(x)) dx ≤ ∫₀^G-1(p)(1 - G(x)) dx all p ε (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.

Original language	English
Pages (from-to)	826-845
Number of pages	20
Journal	Advances in Applied Probability
Volume	34
Issue number	4
DOIs	https://doi.org/10.1239/aap/1037990955
State	Published - Dec 2002

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 10 Reduced Inequalities

Keywords

Economic inequality measure
Empirical TTT transform
Excess wealth order
HNBUE
Increasing convex and concave orders
Lorenz order
NBUE
Right-spread order
Series and parallel systems
Test for 'more NBUE'

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10.1239/aap/1037990955

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abstract = "For nonnegative random variables X and Y we write X ≤TTT Y if ∫0F-1(p)(1-F(x)) dx ≤ ∫0G-1(p)(1 - G(x)) dx all p ε (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.",

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T1 - The total time on test transform and the excess wealth stochastic orders of distributions

AU - Kochar, Subhash C.

AU - Li, Xiaohu

AU - Shaked, Moshe

PY - 2002/12

Y1 - 2002/12

N2 - For nonnegative random variables X and Y we write X ≤TTT Y if ∫0F-1(p)(1-F(x)) dx ≤ ∫0G-1(p)(1 - G(x)) dx all p ε (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.

AB - For nonnegative random variables X and Y we write X ≤TTT Y if ∫0F-1(p)(1-F(x)) dx ≤ ∫0G-1(p)(1 - G(x)) dx all p ε (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.

KW - Economic inequality measure

KW - Empirical TTT transform

KW - Excess wealth order

KW - HNBUE

KW - Increasing convex and concave orders

KW - Lorenz order

KW - NBUE

KW - Right-spread order

KW - Series and parallel systems

KW - Test for 'more NBUE'

UR - https://www.scopus.com/pages/publications/0036950095

UR - https://www.scopus.com/pages/publications/0036950095#tab=citedBy

U2 - 10.1239/aap/1037990955

DO - 10.1239/aap/1037990955

M3 - Article

AN - SCOPUS:0036950095

SN - 0001-8678

VL - 34

SP - 826

EP - 845

JO - Advances in Applied Probability

JF - Advances in Applied Probability

IS - 4

ER -

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

Abstract

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Keywords

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