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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

    as
    1. Mineo, Angelo & Ruggieri, Mariantonietta, 2005. "A Software Tool for the Exponential Power Distribution: The normalp Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i04).
    2. repec:bla:biomet:v:71:y:2015:i:4:p:1081-1089 is not listed on IDEAS
    3. Wolf-Dieter Richter, 2016. "Exact inference on scaling parameters in norm and antinorm contoured sample distributions," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    4. Stuart Rothstein & William Bell & Jayne Patrick & Harry Miller, 1981. "A jackknife test of homogeneity of variance with paired replicates data," Psychometrika, Springer;The Psychometric Society, vol. 46(1), pages 35-40, March.
    5. Kuwana, Yoichi & Kariya, Takeaki, 1991. "LBI tests for multivariate normality in exponential power distributions," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 117-134, October.
    6. Rand R. Wilcox, 1990. "Comparing the Variances of Two Dependent Groups," Journal of Educational and Behavioral Statistics, , vol. 15(3), pages 237-247, September.
    7. Klaus Müller & Wolf-Dieter Richter, 2015. "Exact extreme value, product, and ratio distributions under non-standard assumptions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 1-30, January.
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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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