On the equivalence of the coefficient of variation ordering and the lorenz ordering within two-parameter families

Yugu Xiao, Jing Yao

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

It is well-known that the Lorenz ordering, which is widely used to rank the inequality of income, will lead to the ordering of coefficient of variation. This paper finds that these two stochastic orders are equivalent within several common two-parameter families of distributions including the location-scale family, some scale and shape parameter family. Our finding manifests that once the compared life distributions or income distributions belong to a two-parameter family discussed above, rankings by the Lorenz curve and by the coefficient of variation for inequality generate the same order. Furthermore, a simple general sufficient condition without limiting within two-parameter families for this property is provided. These results could extend application of coefficient of variation, which can be regarded as a proxy of Lorenz curve in many cases for an inequality ranking or orderings of life distributions, even if the life has asymmetric heavy-tail distribution.

Original languageEnglish
Title of host publicationStochastic Models in Reliability, Network Security and System Safety
Subtitle of host publicationEssays Dedicated to Professor Jinhua Cao on the Occasion of His 80th Birthday
PublisherSpringer Verlag
Pages285-294
Number of pages10
ISBN (Electronic)9789811508646
ISBN (Print)9789811508639
DOIs
Publication statusE-pub ahead of print - 16 Oct 2019

Publication series

NameCommunications in Computer and Information Science
Volume1102
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Keywords

  • Coefficient of variation
  • Location-scale family
  • Lorenz order
  • Scale and shape parameter family

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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  • Cite this

    Xiao, Y., & Yao, J. (2019). On the equivalence of the coefficient of variation ordering and the lorenz ordering within two-parameter families. In Stochastic Models in Reliability, Network Security and System Safety: Essays Dedicated to Professor Jinhua Cao on the Occasion of His 80th Birthday (pp. 285-294). (Communications in Computer and Information Science; Vol. 1102). Springer Verlag. https://doi.org/10.1007/978-981-15-0864-6_14