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.
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References
Cuadras, C. M. (2002), Diagonal distributions via orthogonal expansions and tests of independence. Distributions with given marginals and statistical modelling. This volume, p. 35.
Cuadras, C. M. and J. Fortiana (1995), A continuous metric scaling solution for a random variable. J. of Multivariate Analysis 52, 1–14.
Cuadras, C. M. and J. Fortiana (1996), Weighted continuous metric scaling. In: A. K. Gupta and V. L. Girko, (Eds.) Multidimensional Statistical Analysis and Theory of Random Matrices, pp. 27–40. VSP, Zeist, The Netherlands.
Cuadras, C.M. and J. Fortiana (2000), The Importance of Geometry in Multivariate Analysis and some Applications. In: C.R. Rao and G. Szekely (Eds.), Statistics for the 21st Century, pp. 93–108. Marcel Dekker, New York.
Cuadras, C. M. and Y. Lahlou (2000), Some orthogonal expansions for the logistic distribution. Comm. Stat.-Theor. Meth. 29 (12), 2643–2663.
Durbin, J. and Knott, M. (1972), Components of Cramér-von Mises Statistics. I. J. Royal Statist. Soc., B, 34, 290–307.
Liu, Z. (1991), Bootstrapping one way analysis of Rao’s quadratic entropy. Comm. Stat. -Theory Meth. 20, 1683–1703.
Liu, Z. and C. R. Rao (1995), Asymptotic distribution of statistics based on quadratic entropy and bootstrapping. J. Stat. Planning and Inference 43, 1–18.
Rao, C. R. (1982), Diversity: its measurement, decomposition, apportionment and analysis. Sankhya A 44, 1–21.
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Cuadras, C.M., Lahlou, Y. (2002). Principal Components of the Pareto Distribution. In: Cuadras, C.M., Fortiana, J., Rodriguez-Lallena, J.A. (eds) Distributions With Given Marginals and Statistical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0061-0_6
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DOI: https://doi.org/10.1007/978-94-017-0061-0_6
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