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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)...

Extensión del concepto de energía informacional de Onicescu basado en el análisis no estandar.

Leandro Pardo (1985)

Trabajos de Estadística e Investigación Operativa

En esta comunicación, a partir del concepto de energía informacional de Onicescu para variables aleatorias discretas, se da el concepto de energía informacional para cualquier tipo de variables aleatorias como una extensión del anterior basándonos en el análisis no estándar de Robinson (1960). Se estudian sus propiedades y se analiza, en particular, su comportamiento con respecto a la energía informacional de Onicescu en caso de variables aleatorias continuas.

Extensions of the Frisch-Waugh-Lovell Theorem

Jürgen Groß, Simo Puntanen (2005)

Discussiones Mathematicae Probability and Statistics

In this paper we introduce extensions of the so-called Frisch-Waugh-Lovell Theorem. This is done by employing the close relationship between the concept of linear sufficiency and the appropriate reduction of linear models. Some specific reduced models which demonstrate alternatives to the Frisch-Waugh-Lovell procedure are discussed.

Extraction of fuzzy logic rules from data by means of artificial neural networks

Martin Holeňa (2005)

Kybernetika

The extraction of logical rules from data has been, for nearly fifteen years, a key application of artificial neural networks in data mining. Although Boolean rules have been extracted in the majority of cases, also methods for the extraction of fuzzy logic rules have been studied increasingly often. In the paper, those methods are discussed within a five-dimensional classification scheme for neural-networks based rule extraction, and it is pointed out that all of them share the feature of being...

Extrapolation in fractional autoregressive models

Jiří Anděl, Georg Neuhaus (1998)

Kybernetika

The naïve and the least-squares extrapolation are investigated in the fractional autoregressive models of the first order. Some explicit formulas are derived for the one and two steps ahead extrapolation.

Extrapolations in non-linear autoregressive processes

Jiří Anděl, Václav Dupač (1999)

Kybernetika

We derive a formula for m -step least-squares extrapolation in non-linear AR ( p ) processes and compare it with the naïve extrapolation. The least- squares extrapolation depends on the distribution of white noise. Some bounds for it are derived that depend only on the expectation of white noise. An example shows that in general case the difference between both types of extrapolation can be very large. Further, a formula for least-squares extrapolation in multidimensional non-linear AR( p ) process is derived....

Extremal and additive processes generated by Pareto distributed random vectors

Kosto V. Mitov, Saralees Nadarajah (2014)

ESAIM: Probability and Statistics

Pareto distributions are most popular for modeling heavy tailed data. Here, we obtain weak limits of a sequence of extremal and a sequence of additive processes constructed by a series of Bernoulli point processes with bivariate Pareto space components. For the limiting processes we derive the one dimensional distributions in explicit forms. Some of the main properties of these distributions are also proved.

Extremal behaviour of stationary processes: the calibration technique in the extremal index estimation

D. Prata Gomes, Maria Manuela Neves (2010)

Discussiones Mathematicae Probability and Statistics

Classical extreme value methods were derived when the underlying process is assumed to be a sequence of independent random variables. However when observations are taken along the time and/or the space the independence is an unrealistic assumption. A parameter that arises in this situation, characterizing the degree of local dependence in the extremes of a stationary series, is the extremal index, θ. In several areas such as hydrology, telecommunications, finance and environment, for example, the...

Extremal (in)dependence of a maximum autoregressive process

Marta Ferreira (2013)

Discussiones Mathematicae Probability and Statistics

Maximum autoregressive processes like MARMA (Davis and Resnick, [5] 1989) or power MARMA (Ferreira and Canto e Castro, [12] 2008) have singular joint distributions, an unrealistic feature in most applications. To overcome this pitfall, absolute continuous versions were presented in Alpuim and Athayde [2] (1990) and Ferreira and Canto e Castro [14] (2010b), respectively. We consider an extended version of absolute continuous maximum autoregressive processes that accommodates both asymptotic tail...

Extreme distribution functions of copulas

Manuel Úbeda-Flores (2008)

Kybernetika

In this paper we study some properties of the distribution function of the random variable C(X,Y) when the copula of the random pair (X,Y) is M (respectively, W) – the copula for which each of X and Y is almost surely an increasing (respectively, decreasing) function of the other –, and C is any copula. We also study the distribution functions of M(X,Y) and W(X,Y) given that the joint distribution function of the random variables X and Y is any copula.

Extreme order statistics in an equally correlated Gaussian array

Mateusz Wiśniewski (1994)

Applicationes Mathematicae

This paper contains the results concerning the weak convergence of d-dimensional extreme order statistics in a Gaussian, equally correlated array. Three types of limit distributions are found and sufficient conditions for the existence of these distributions are given.

Extreme value distributions for dependent jointly ln,p-symmetrically distributed random variables

K. Müller, W.-D. Richter (2016)

Dependence Modeling

A measure-of-cone representation of skewed continuous ln,p-symmetric distributions, n ∈ N, p > 0, is proved following the geometric approach known for elliptically contoured distributions. On this basis, distributions of extreme values of n dependent random variables are derived if the latter follow a joint continuous ln,p-symmetric distribution. Light, heavy, and extremely far tails as well as tail indices are discussed, and new parameters of multivariate tail behavior are introduced.

Extreme values and kernel estimates of point processes boundaries

Stéphane Girard, Pierre Jacob (2004)

ESAIM: Probability and Statistics

We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.

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