Kurtosis: Definition and Properties

International audienceIn 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