Modelling of skewness measure distribution

Margus  Pihlak

doi:https://doi.org/10.59170/stattrans-2014-010

Modelling of skewness measure distribution

Margus Pihlak Tallinn University of Technology (Estonia), Department of Mathematics, Ehitajate tee 5 19086 Tallinn. Statistics in Transition new series, vol. 15, 2014, 1, pages: 145-152 Published online: 3 March 2014 https://doi.org/10.59170/stattrans-2014-010

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ABSTRACT

In this paper the distribution of random variable skewness measure is modelled. Firstly, we present some results of matrix algebra useful in multivariate statistical analyses. Then, we apply the central limit theorem on modelling of skewness measure distribution. Finally, we give an idea for finding the confidence intervals of statistical model residuals' asymmetry measure

KEYWORDS

central limit theorem, multivariate skewness measure, skewness measure distribution, statistical model residuals.

REFERENCES

ANDERSON, T. W., (2003). An Introduction to Multivariate Statistical Analysis.Wiley Interscience.

HARVILLE, A., (1997). Matrix Algebra from a Statistician’s Perspective. Springer, New York.

KLAR, B., (2002). A Treatment of Multivariate Skewness, Kurtosis, and Related Statistics. Journal of Multivariate Analysis, 83, 141–165.

KOLLO, T., (1991). Matrix Derivative in Multivariate Statistics. Tartu University Press, Tartu (in Russian).

KOLLO, T., SRIVASTAVA, M. S., (2004). Estimation and testing of parameters in multivariate Laplace distribution. Comm. Statist., 33, 2363–2687.

KOLLO, T., VON ROSEN, D., (2005). Advanced Multivariate Statistics with Matrices. Springer, Dordrecht.

KOLLO, T., (2008). Multivariate skewness and kurtosis measures with an application in ICA. Journal of Multivariate Analyses, 99, 2328–2338.

MacRAE, E. C., (1974). Matrix derivatives with an application to an adaptive linear decision problem. Ann. Statist., 2, 337–346.

MARDIA, K. V., (1970). Measures of multivariate skewness and kurtosis measures with applications. Biometrika, 57, 519–530.

MORI, T. F., ROHATGI, V. K., SZÉKELY., (1993). On multivariate skewness and kurtosis. Theory Probab. Appl, 38, 547–551.

NEUDECKER, H., (1969). Some theorems on matrix differentiations with special reference to Kronecker matrix products. Journal of the American Statistical Association, 64, 953–963.

PARRING, A-M., (1979). Estimation asymptotic characteristic function of sample (in Russian). Acta et Commetationes Universitatis Tartuensis de Mathematica, 492, 86–90.

PIHLAK, M., (2004). Matrix integral. Linear Algebra and its Applications, 388, 315–325