The observed total time on test and the observed excess wealth

Xiaohu Li; Moshe Shaked

doi:10.1016/j.spl.2004.03.003

The observed total time on test and the observed excess wealth

Xiaohu Li
, Moshe Shaked

Department of Mathematical Sciences

University of Arizona

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

18 Scopus citations

Abstract

Let X be a nonnegative random variable with mean μ≤∞, and let T_X be the total time on test transform of X. It has been observed in the literature that the inverse of T_X is a distribution function with support (0,μ). In this paper, we identify the random variable that has this distribution, and we study some of its properties. We also study an analogous random variable that is based on what is called the excess wealth transform.

Original language	English
Pages (from-to)	247-258
Number of pages	12
Journal	Statistics and Probability Letters
Volume	68
Issue number	3
DOIs	https://doi.org/10.1016/j.spl.2004.03.003
State	Published - 1 Jul 2004

Keywords

HNBUE
IFR
IFRA
NBUE
Pareto distribution
Stochastic orders

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10.1016/j.spl.2004.03.003

Cite this

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abstract = "Let X be a nonnegative random variable with mean μ≤∞, and let TX be the total time on test transform of X. It has been observed in the literature that the inverse of TX is a distribution function with support (0,μ). In this paper, we identify the random variable that has this distribution, and we study some of its properties. We also study an analogous random variable that is based on what is called the excess wealth transform.",

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AU - Shaked, Moshe

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AB - Let X be a nonnegative random variable with mean μ≤∞, and let TX be the total time on test transform of X. It has been observed in the literature that the inverse of TX is a distribution function with support (0,μ). In this paper, we identify the random variable that has this distribution, and we study some of its properties. We also study an analogous random variable that is based on what is called the excess wealth transform.

KW - HNBUE

KW - IFR

KW - IFRA

KW - NBUE

KW - Pareto distribution

KW - Stochastic orders

UR - https://www.scopus.com/pages/publications/3042625353

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U2 - 10.1016/j.spl.2004.03.003

DO - 10.1016/j.spl.2004.03.003

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VL - 68

SP - 247

EP - 258

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 3

ER -

The observed total time on test and the observed excess wealth

Abstract

Keywords

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