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Auditing Shaked and Shanthikumar’s ‘excess wealth’

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  • Nozer Singpurwalla
  • Anna Gordon

Abstract

A notion called “excess wealth” was introduced by Shaked and Shanthikumar around 1998 (Probab. Eng. Inf. Sci. 12:1–23, 1998 ). Subsequent to this, much has been written on it, mostly by Shaked and his colleagues; see Sordo (Insur. Math. Econ. 45(3):466–469, 2009 ) for a recent review. These works have appeared in the literatures of reliability theory and stochastic orderings. Since the term excess wealth connotes a measure of income inequality—much like its dual, poverty—it should have had an impact in economics and the econometric literature. This, it appears is not the case, at least to the extent that it should be. The purpose of this paper is to investigate the above disconnect by looking at the notion of excess wealth more carefully, but keeping in mind the angle of economics and income. Our conclusion is that an alternative definition of excess wealth better encapsulates what one means by a colloquial use of the term. Our motivation for being attracted to this topic arises from two angles. The first is that the stochastics of diagnostic and threat detection tests, in which we have an interest, has a strong bearing on indices of concentration like the Lorenz Curve, the Gini index, and the entropy. Thus the notion of excess wealth, which conveys a sense of income concentration should also be relevant to diagnostics. The second motivation is to honor Moshe Shaked, a prolific researcher and a friend of the first author, by developing a paper based on an idea that is co-attributed to him. Copyright Springer Science+Business Media, LLC 2014

Suggested Citation

  • Nozer Singpurwalla & Anna Gordon, 2014. "Auditing Shaked and Shanthikumar’s ‘excess wealth’," Annals of Operations Research, Springer, vol. 212(1), pages 3-19, January.
    • Handle: RePEc:spr:annopr:v:212:y:2014:i:1:p:3-19:10.1007/s10479-012-1202-6
    DOI: 10.1007/s10479-012-1202-6
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    References listed on IDEAS

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    1. Mahesh Chandra & Nozer D. Singpurwalla, 1981. "Relationships Between Some Notions Which are Common to Reliability Theory and Economics," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 113-121, February.
    2. Sordo, Miguel A., 2009. "Comparing tail variabilities of risks by means of the excess wealth order," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 466-469, December.
    3. Sarabia, José María, 2008. "A general definition of the Leimkuhler curve," Journal of Informetrics, Elsevier, vol. 2(2), pages 156-163.
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