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Multivariate [theta]-generalized normal distributions

Author

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  • Goodman, Irwin R.
  • Kotz, Samuel

Abstract

A new family of continuous multivariate distributions is introduced, generalizing the canonical form of the multivariate normal distribution. The well-known univariate version of this family, as developed by Box, Tiao and Lund, among others, has proven a valuable tool in Bayesian analysis and robustness studies, as well as serving as a unified model for least [theta]'s and maximum likelihood estimates. The purpose of the family introduced here is to extend, to a degree of generality which will permit practical applications, the useful role played by the univariate family to a multidimensional setting.

Suggested Citation

  • Goodman, Irwin R. & Kotz, Samuel, 1973. "Multivariate [theta]-generalized normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 3(2), pages 204-219, June.
    • Handle: RePEc:eee:jmvana:v:3:y:1973:i:2:p:204-219
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    Citations

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    Cited by:

    1. Norbert Henze & María Dolores Jiménez-Gamero, 2019. "A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 499-521, June.
    2. Vladimír Lacko & Radoslav Harman, 2012. "A conditional distribution approach to uniform sampling on spheres and balls in L p spaces," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 939-951, October.
    3. Moneta, Alessio & Pallante, Gianluca, 2022. "Identification of Structural VAR Models via Independent Component Analysis: A Performance Evaluation Study," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    4. Alex Dytso & Ronit Bustin & H. Vincent Poor & Shlomo Shamai, 2018. "Analytical properties of generalized Gaussian distributions," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-40, December.
    5. Fabian Sinz & Matthias Bethge, 2013. "Temporal Adaptation Enhances Efficient Contrast Gain Control on Natural Images," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-13, January.
    6. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.

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