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A characterization of the pareto distribution
Canadian Journal of Statistics, 1973AbstractSuppose that in a random sample of size n from a population with probability density function f(x), the order statistics are X(1) <x(2) <…<x(n). It is proved that a necessary and sufficient condition for f (x) to be a Pareto density function is that the statistics X(r) and X(s)/X(r) ≤ r < s ≤ n) are independent.
Ahsanullah, M., Kabir, A. B. M. Lutful
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Pareto and Generalized Pareto Distributions
2008More than one hundred years after its introduction, Pareto’s proposed model for fitting income distributions continues to be heavily used. A variety of generalizations of this model have been proposed including discrete versions, together with natural multivariate extensions.
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Exponentiated Pareto distributions
Statistics, 2005Most Pareto distributions are defined on one side of the real line. For wider applicability, we introduce five exponentiated Pareto distributions and derive several of their properties including the moment generating function, expectation, variance, skewness, kurtosis, Shannon entropy, and the Renyi entropy.
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Statistics, 2008
In this paper, a four-parameter beta-Pareto distribution is defined and studied. Various properties of the distribution are discussed. The distribution is found to be unimodal and has either a unimodal or a decreasing hazard rate. The expressions for the mean, mean deviation, variance, skewness, kurtosis and entropies are obtained.
Alfred Akinsete, Felix Famoye, Carl Lee
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In this paper, a four-parameter beta-Pareto distribution is defined and studied. Various properties of the distribution are discussed. The distribution is found to be unimodal and has either a unimodal or a decreasing hazard rate. The expressions for the mean, mean deviation, variance, skewness, kurtosis and entropies are obtained.
Alfred Akinsete, Felix Famoye, Carl Lee
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Soft Computing - A Fusion of Foundations, Methodologies and Applications, 2021
Fatma Gül Akgül
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Fatma Gül Akgül
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Bivariate distributions with pareto conditionals
Statistics & Probability Letters, 1987For a fixed \(\alpha >0\), the totality of bivariate densities with all conditionals being of the Pareto (\(\alpha)\) form is identified. The resulting family is of the form \[ f(x,y)\propto [1+\lambda_ 1x+\lambda_ 2y+\phi \lambda_ 1\lambda_ 2xy]^{-(\alpha +1)} \] for suitable choices of \(\lambda_ 1\), \(\lambda_ 2\) and \(\phi\).
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Pareto ordering of distributions
Journal of Mathematical Economics, 1978Abstract In this paper, the state of an economy is described by a production plan and a distribution on the product space of agents' characteristics and the commodity space. An ordering on the set of states will be introduced and after a study of the structure of this ordering it will be shown that the close relationship between price equilibria and ...
Reif, Nicolaus, Wiesmeth, Hans
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1990
Using certain data on personal income, V. Pareto (1897) plotted income on the abscissa and the number of people who received more than that on the ordinate of logarithmic paper and found a roughly linear relation. This Pareto distribution or ‘Pareto law’ may be written as $$x = a\,{y^{ - \alpha }}\,{\text{or}}\,\log \,x = a' - \alpha \,\log \,y$$
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Using certain data on personal income, V. Pareto (1897) plotted income on the abscissa and the number of people who received more than that on the ordinate of logarithmic paper and found a roughly linear relation. This Pareto distribution or ‘Pareto law’ may be written as $$x = a\,{y^{ - \alpha }}\,{\text{or}}\,\log \,x = a' - \alpha \,\log \,y$$
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On q-pareto distribution: some properties and application to earthquakes
, 2021E. Barra, P. Vega-Jorquera
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