TY - CHAP
T1 - On the equivalence of the coefficient of variation ordering and the lorenz ordering within two-parameter families
AU - Xiao, Yugu
AU - Yao, Jing
PY - 2019/10/16
Y1 - 2019/10/16
N2 - 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.
AB - 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.
KW - Coefficient of variation
KW - Location-scale family
KW - Lorenz order
KW - Scale and shape parameter family
UR - http://www.scopus.com/inward/record.url?scp=85074641398&partnerID=8YFLogxK
U2 - 10.1007/978-981-15-0864-6_14
DO - 10.1007/978-981-15-0864-6_14
M3 - Chapter
AN - SCOPUS:85074641398
SN - 9789811508639
T3 - Communications in Computer and Information Science
SP - 285
EP - 294
BT - Stochastic Models in Reliability, Network Security and System Safety
PB - Springer
ER -