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Statistical reasoning in dependent p-generalized elliptically contoured distributions and beyond

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  • Wolf-Dieter Richter

    (University of Rostock, Institute of Mathematics)

Abstract

First, likelihood ratio statistics for checking the hypothesis of equal variances of two-dimensional Gaussian vectors are derived both under the standard σ 1 2 , σ 2 2 , ϱ $\left (\sigma ^{2}_{1},\sigma ^{2}_{2},\varrho \right)$ -parametrization and under the geometric (a,b,α)-parametrization where a 2 and b 2 are the variances of the principle components and α is an angle of rotation. Then, the likelihood ratio statistics for checking the hypothesis of equal scaling parameters of principle components of p-power exponentially distributed two-dimensional vectors are considered both under independence and under rotational or correlation type dependence. Moreover, the role semi-inner products play when establishing various likelihood equations is demonstrated. Finally, the dependent p-generalized polar method and the dependent p-generalized rejection-acceptance method for simulating star-shaped distributed vectors are presented.

Suggested Citation

  • Wolf-Dieter Richter, 2017. "Statistical reasoning in dependent p-generalized elliptically contoured distributions and beyond," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    • Handle: RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0074-3
    DOI: 10.1186/s40488-017-0074-3
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    References listed on IDEAS

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    Cited by:

    1. Klaus Müller & Wolf-Dieter Richter, 2019. "On p-generalized elliptical random processes," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-37, December.

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