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Assessing the effect of kurtosis deviations from Gaussianity on conditional distributions

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Gómez Villegas, Miguel A. and Main Yaque, Paloma and Navarro, H. and Susi, R. (2013) Assessing the effect of kurtosis deviations from Gaussianity on conditional distributions. Applied Mathematics and Computation, 219 (21). pp. 10499-10505. ISSN 0096-3003

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Official URL: http://www.sciencedirect.com/science/article/pii/S0096300313004463


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Abstract

The multivariate exponential power family is considered for n-dimensional random variables, Z, with a known partition Z equivalent to (Y, X) of dimensions p and n - p, respectively, with interest focusing on the conditional distribution Y vertical bar X. An infinitesimal variation of any parameter of the joint distribution produces perturbations in both the conditional and marginal distributions. The aim of the study was to determine the local effect of kurtosis deviations using the Kullback-Leibler divergence measure between probability distributions. The additive decomposition of this measure in terms of the conditional and marginal distributions, Y vertical bar X and X, is used to define a relative sensitivity measure of the conditional distribution family {Y vertical bar X = x}. Finally, simulated results suggest that for large dimensions, the measure is approximately equal to the ratio p/n, and then the effect of non-normality with respect to kurtosis depends only on the relative size of the variables considered in the partition of the random vector.


Item Type:Article
Uncontrolled Keywords:Multivariate exponential power distributions; Kurtosis; Kullback-Leibler divergence; Relative sensitivity
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:22607
Deposited On:29 Jul 2013 08:41
Last Modified:26 Jun 2018 06:30

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