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Principal components of the Pareto distribution. (English) Zbl 1137.62346
Cuadras, Carles M. (ed.) et al., Distributions with given marginals and statistical modelling. Papers presented at the meeting, Barcelona, Spain, July 17–20, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0914-3/hbk). 43-50 (2002).
Summary: Let $$X$$ be a random variable with distribution function $$F$$, the Pareto distribution. Eigendecomposition of the kernel $$F(s)\wedge F(t)-F(s)F(t)$$ 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.
For the entire collection see [Zbl 1054.62002].

MSC:
 62H25 Factor analysis and principal components; correspondence analysis 33C90 Applications of hypergeometric functions 34A05 Explicit solutions, first integrals of ordinary differential equations