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This impressive collection from a few of today’s prime distributional analysts presents an outline quite a lot of fiscal, statistical and sociological relationships which have been unfolded for medical learn by means of the paintings of 2 turn-of-the-20th-century economists: C. Gini and M. O. Lorenz.
The authors contain such figues as Barry Arnold and Frank Cowell and the ensuing ebook merits its position at the bookshelf of great mathematical economists everywhere.
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Extra resources for Advances on Income Inequality and Concentration Measures
2 The axiomatic approach It might seem that the axiomatic approach is somewhat arbitrary. However, one of the arguments of this chapter is that there is a commonality of axioms across a number of topics that yield important insights on the connections between various principles of distributional analysis. To begin with there are a few basic axioms that are frequently invoked to deﬁne the structure of evaluation functions and rankings. They are used so frequently that it makes sense to state a version of them here, before we have examined any of the speciﬁc distributional issues.
E. R will be small. Nayak and Christman (1992) show that for any r = 1, 2, . , n the quantity Pp(R ≤ r), is indeed a Schur convex function of p. From this it follows that the expected number of species represented in the sample, Ep (R), is a Schur concave function of p. Consequently most of the estimates of v that are quite sensible assuming equal catchability will be negatively biased with the bias increasing as the variability in catchability increases. It is possible to reinterpret these computations in the context of a simple random sample taken with replacement from a population broken into subpopulations of various sizes.
Ebert and Moyes (2000) provide an axiomatization of individual deprivation whereby the index is to be deﬁned for all logically possible reference groups for a given N. As an alternative Bossert and D’Ambrosio (2006) axiomatize the Yitzhaki index using an approach that diﬀers from Ebert and Moyes (2000) in the way the reference group of an individual is to be represented. Although it is otherwise similar to Ebert and Moyes (2000), some of the other axioms have to be modiﬁed or replaced as a result of this alternative way of characterizing the reference group.