By Gianni Betti, Achille Lemmi
This impressive collection from a few of today’s top distributional analysts presents an outline a variety of fiscal, statistical and sociological relationships which have been spread out for clinical examine 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 e-book merits its position at the bookshelf of significant mathematical economists everywhere.
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Extra info for Advances on Income Inequality and Concentration Measures
4 Dalton’s key principle In his important paper on desirable properties of income inequality measures, Dalton (1920) proposed four principles. The important one for our purposes is the one that says that, if we take a small amount from an individual in a population and give it to a relatively poorer individual in the population, the result will be a decrease in inequality. In other words, Robin Hood, in taking from the rich and giving to the poor, is indeed reducing inequality. In honor of the celebrated hero of Sherwood Forest, we will call this the Robin Hood principle (it is also known as the Dalton or the PigouDalton principle) and the operation as a Robin Hood transfer.
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.
We will say that T has a phase-type distribution of order n if n is the smallest integer such that the distribution can be identiﬁed with the time to absorption in a chain with n transient and one absorbing state. e. d. exponential (l) random variables. e. we have a = (1, 0, . , 0)) and progresses 20 Introduction sequentially through the states 2,3, . , n + 1 spending an independent exponential (l) time in each transient state. Denote such a simple phase-type random variable by T*. It is evident that phase-type distributions of order n with the same mean can exhibit considerable diﬀerences in their variability.
Advances on Income Inequality and Concentration Measures by Gianni Betti, Achille Lemmi