Principal Components of the Pareto Distribution

Carles M. Cuadras and Younes Lahlou
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Carles M. Cuadras: University of Barcelona
Younes Lahlou: University of Barcelona

A chapter in Distributions With Given Marginals and Statistical Modelling, 2002, pp 43-50 from Springer

Abstract: Abstract Abstract Let X be a random variable with distribution function F, the Pareto distribution. Eigendecomposition of the kernel F(s) ∧ F(t) - F(s)F(t) allows us to expand X as a series of principal components. The expansion of X for the general Pareto distribution can be expressed using the cylinder function, but may not be straightforward. We find the complete solution for a particular Pareto distribution, which can be expressed in terms of Bessel and trigonometric functions. A comparison with the exponential distribution is performed.

Keywords: orthogonal expansions; continuous scaling; shape of a distribution; Bessel-Lommel equation (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0061-0_6

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DOI: 10.1007/978-94-017-0061-0_6

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