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Principal Components of the Pareto Distribution

In: Distributions With Given Marginals and Statistical Modelling

Author

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  • Carles M. Cuadras

    (University of Barcelona)

  • Younes Lahlou

    (University of Barcelona)

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.

Suggested Citation

  • Carles M. Cuadras & Younes Lahlou, 2002. "Principal Components of the Pareto Distribution," Springer Books, in: Carles M. Cuadras & Josep Fortiana & José A. Rodriguez-Lallena (ed.), Distributions With Given Marginals and Statistical Modelling, pages 43-50, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0061-0_6
    DOI: 10.1007/978-94-017-0061-0_6
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