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Estudio asintótico de una clase de índices de desigualdad muestrales.

María Angeles Gil Alvarez, Covadonga Caso, Pedro Gil Alvarez (1989)

Trabajos de Estadística

En la literatura sobre la cuantificación de la Desigualdad de una población en relación con cierta variable económica (renta, capital, etc.) se han establecido diferentes medidas, entre las cuales por su operatividad y caracterización axiomática merecen mención especial los llamados "índices de desigualdad aditivamente descomponibles" (que incluyen los conocidos índices de Theil y de la varianza normalizada).En este trabajo desarrollamos un estudio del comportamiento asintótico de dichos índices...

Exponential wealth distribution : a new approach from functional iteration theory*

Ricardo López-Ruiz, José-Luis López, Xavier Calbet (2012)

ESAIM: Proceedings

Different approaches are possible in order to derive the exponential regime in statistical systems. Here, a new functional equation is proposed in an economic context to explain the wealth exponential distribution. Concretely, the new iteration [1] given by f n + 1 ( x ) = u + v > x f n ( u ) f n ( v ) u + v d u d v . It is found that the exponential distribution is a stable fixed point of this functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions)...

Formes et propriétés des indices d'inégalité entre proportions

Antoine Valeyre (1995)

Mathématiques et Sciences Humaines

Cet article porte sur les indicateurs qui permettent de comparer les inégalités de proportions entre deux catégories. Après avoir précisé les propriétés qui caractérisent la définition d'indices d'inégalité entre deux proportions, il analyse celles qu'il est souhaitable de leur appliquer, notamment les propriétés de cohérence ou d'homogénéité dont il montre l'incompatibilité. Il examine différents modes de construction d'indices d'inégalité : à partir de mesures, de distances, de caractéristiques...

Gini indices and the moments of the share density function

Petr Zizler (2014)

Applications of Mathematics

The expected value of the share density of the income distribution can be expressed in terms of the Gini index. The variance of the share density of the income distribution is interesting because it gives a relationship between the first and the second order Gini indices. We find an expression for this variance and, as a result, we obtain some nontrivial bounds on these Gini indices. We propose new statistics on the income distribution based on the higher moments of the share density function. These...

Models for option pricing based on empirical characteristic function of returns

Karol Binkowski, Andrzej Kozek (2010)

Banach Center Publications

The standard Merton-Black-Scholes formula for European Option pricing serves only as approximation to real values of options. More advanced extensions include applications of Lévy processes and are based on characteristic functions, which are more convenient to use than the corresponding probability distributions. We found one of the Lewis (2001) general theoretical formulae for option pricing based on characteristic functions particularly suitable for a statistical approach to option pricing. By...

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