Decomposition of symmetric multivariate density function

Kiyotaka Iki; Kouji Tahata; Sadao Tomizawa

doi:10.55937/sut/1360240217

June 2012 Decomposition of symmetric multivariate density function

Kiyotaka Iki, Kouji Tahata, Sadao Tomizawa

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SUT J. Math. 48(2): 199-211 (June 2012). DOI: 10.55937/sut/1360240217

Abstract

For a $T$ -variate density function, the present article defines the quasi-symmetry of order $k( < T)$ and the marginal symmetry of order $k$ , and gives the theorem that the density function is $T$ -variate permutation symmetric if and only if it is quasi-symmetric and marginal symmetric of order $k$ . The theorem is illustrated for the multivariate normal density function.

Acknowledgements

The authors would like to express our sincere thanks to a referee for the meaningful comments.

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Kiyotaka Iki. Kouji Tahata. Sadao Tomizawa. "Decomposition of symmetric multivariate density function." SUT J. Math. 48 (2) 199 - 211, June 2012. https://doi.org/10.55937/sut/1360240217