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BY-NC-ND 3.0 license Open Access Published by De Gruyter August 27, 2008

Approximation of multivariate distribution functions

  • Margus Pihlak EMAIL logo
From the journal Mathematica Slovaca

Abstract

In the paper the unknown distribution function is approximated with a known distribution function by means of Taylor expansion. For this approximation a new matrix operation — matrix integral — is introduced and studied in [PIHLAK, M.: Matrix integral, Linear Algebra Appl. 388 (2004), 315–325]. The approximation is applied in the bivariate case when the unknown distribution function is approximated with normal distribution function. An example on simulated data is also given.

[1] ANDERSON, T. W.: An Introduction to Multivariate Statistical Analysis, Wiley, New York, 2003. Search in Google Scholar

[2] CORNISH, E. A.— FISHER, R. A.: Moments and cumulants in the specification of distribution, Rev. Inst. Int. Stat. 5 (1937), 307–322. http://dx.doi.org/10.2307/140090510.2307/1400905Search in Google Scholar

[3] KOLLO, T.: Matrix Derivative in Multivariate Statistics, Tartu University Press, Tartu, 1991 (Russian). Search in Google Scholar

[4] KOLLO, T.— VON ROSEN, D.: Approximating by the Wishart distribution, Ann. Inst. Statist. Math. 47 (1995), 767–783. http://dx.doi.org/10.1007/BF0185654610.1007/BF01856546Search in Google Scholar

[5] MACRAE, E. C.: Matrix derivatives with an applications to an adaptive linear decision problem, Ann. Statist. 7 (1974), 381–394 10.1214/aos/1176342667Search in Google Scholar

[6] NEUDECKER, H.: Some theorems on matrix differentiations with special reference to Kronecker matrix products, J. Amer. Statist. Assoc. 64 (1969), 953–963. http://dx.doi.org/10.2307/228347610.2307/2283476Search in Google Scholar

[7] PIHLAK, M.: Matrix integral, Linear Algebra Appl. 388 (2004), 315–325 http://dx.doi.org/10.1016/j.laa.2004.02.04210.1016/j.laa.2004.02.042Search in Google Scholar

Published Online: 2008-8-27
Published in Print: 2008-10-1

© 2008 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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