Inverse stochastic dominance, inequality measurement and Gini indices

2002 ◽  
Vol 77 (S1) ◽  
pp. 119-161 ◽  
Author(s):  
Claudio Zoli
Keyword(s):  
Stochastic Dominance ◽  
Inequality Measurement ◽  
Inverse Stochastic Dominance

Inverse Stochastic Dominance and its Application in Production Process Control

2002 ◽  
pp. 362-376
Author(s):  
Maciej Nowak ◽  
Tadeusz Trzaskalik ◽  
Grażyna Trzpiot ◽  
Kazimierz Zaraś
Keyword(s):  
Process Control ◽  
Production Process ◽  
Stochastic Dominance ◽  
Inverse Stochastic Dominance

scholarly journals Inverse Stochastic Dominance, Majorization, and Mean Order Statistics

2010 ◽  
Vol 47 (1) ◽  
pp. 277-292 ◽  
Author(s):  
Jesús De La Cal ◽  
Javier Cárcamo
Keyword(s):  
Social Inequality ◽  
Order Statistics ◽  
Stochastic Dominance ◽  
Natural Extension ◽  
Stochastic Order ◽  
Stochastic Orderings ◽  
Natural Extensions ◽  
Weak Majorization ◽  
Two Populations ◽  
Inverse Stochastic Dominance

The inverse stochastic dominance of degree r is a stochastic order of interest in several branches of economics. We discuss it in depth, the central point being the characterization in terms of the weak r-majorization of the vectors of expected order statistics. The weak r-majorization (a notion introduced in the paper) is a natural extension of the classical (reverse) weak majorization of Hardy, Littlewood and Pòlya. This work also shows the equivalence between the continuous majorization (of higher order) and the discrete r-majorization. In particular, our results make it clear that the cases r = 1, 2 differ substantially from those with r ≥ 3, a fact observed earlier by Muliere and Scarsini (1989), among other authors. Motivated by this fact, we introduce new stochastic orderings, as well as new social inequality indices to compare the distribution of the wealth in two populations, which could be considered as natural extensions of the first two dominance rules and the S-Gini indices, respectively.

scholarly journals Inverse Stochastic Dominance, Majorization, and Mean Order Statistics

2010 ◽  
Vol 47 (01) ◽  
pp. 277-292 ◽  
Author(s):  
Jesús De La Cal ◽  
Javier Cárcamo
Keyword(s):  
Social Inequality ◽  
Order Statistics ◽  
Stochastic Dominance ◽  
Natural Extension ◽  
Stochastic Order ◽  
Stochastic Orderings ◽  
Natural Extensions ◽  
Weak Majorization ◽  
Two Populations ◽  
Inverse Stochastic Dominance

The inverse stochastic dominance of degree r is a stochastic order of interest in several branches of economics. We discuss it in depth, the central point being the characterization in terms of the weak r-majorization of the vectors of expected order statistics. The weak r-majorization (a notion introduced in the paper) is a natural extension of the classical (reverse) weak majorization of Hardy, Littlewood and Pòlya. This work also shows the equivalence between the continuous majorization (of higher order) and the discrete r-majorization. In particular, our results make it clear that the cases r = 1, 2 differ substantially from those with r ≥ 3, a fact observed earlier by Muliere and Scarsini (1989), among other authors. Motivated by this fact, we introduce new stochastic orderings, as well as new social inequality indices to compare the distribution of the wealth in two populations, which could be considered as natural extensions of the first two dominance rules and the S-Gini indices, respectively.

Third-degree stochastic dominance and inequality measurement

2008 ◽  
Vol 7 (3) ◽  
pp. 249-268 ◽  
Author(s):  
Michel Le Breton ◽  
Eugenio Peluso
Keyword(s):  
Stochastic Dominance ◽  
Inequality Measurement
Sign in / Sign up

Export Citation Format

Share Document