Far East Journal of Theoretical Statistics
Volume 35, Issue 2, Pages 95 - 114
(May 2011)
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ON THE FAMILY OF THE g -ORDERED NORMAL DISTRIBUTIONS
Christos P. Kitsos and Thomas L. Toulias
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Abstract: In this paper, a generalized form of the multivariate normal distribution has been adopted for investigation. This generalization has been emerged from a Logarithmic Sobolev Inequality approach. This introduced family of distributions result normal, uniform and Laplace distributions for certain values of the extra parameter. The moments of this distribution family are evaluated and extensively studied. Their behaviour, with respect to the involved extra parameter, is also examined and discussed, as far as the variance and kurtosis are concerned. This extra parameter influences the shape of the members of the family and, therefore, “heavy-tailed” distributions can be obtained. |
Keywords and phrases: multivariate uniform distribution, multivariate Laplace distribution, moments behaviour. |
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