FUSION'98 International Conference

Kurtosis: Definition and Properties.

Ali MANSOUR
BMC Research Center (RIKEN),
2271-130, Anagahora, Shimoshidami, Moriyama-ku, Nagoya 463 (JAPAN)

and
Christian JUTTEN
INPG - LIS
46, avenue F\'{e}lix Viallet, 38031 Grenoble Cedex


and
Noboru OHNISHI
BMC Research Center (RIKEN),
2271-130, Anagahora, Shimoshidami, Moriyama-ku, Nagoya 463 (JAPAN)

Abstract
In various studies on blind separation of sources, one assumes that sources have the same
sign of kurtosis. In fact, this assumption seems very strong and in this paper we studied
relation between signal distribution and the sign of the kurtosis. A theoretical result has
been found in a simple case. However, for more complex distributions, the kurtosis sign
cannot be predicted and may change with parameters. The results give theoretical
explanation to tricks, like non-permanent adaptation, used in non stationary situations.

Keywords: kurtosis, high order statistics, blind identification and separation, probability density function.