Fisher Information and Uncertainty Principle for Skew-Gaussian Random Variables

Fisher information is a measure to quantify information and estimate system-defining parameters. The scaling and uncertainty properties of this measure, linked with Shannon entropy, are useful to characterize signals through the Fisher-Shannon plane. In addition, several non-gaussian distributions have been exemplified, given that assuming gaussianity in evolving systems is unrealistic, and the derivation of distributions that addressed asymmetry and heavy-tails is more suitable. The latter has motivated studying Fisher information and the uncertainty principle for skew-gaussian random variables for this paper. We describe the skew-gaussian distribution effect on uncertainty principle, from which the Fisher information, the Shannon entropy power, and the Fisher divergence are derived. Results indicate that flexibility of skew-gaussian distribution with a shape parameter allows deriving explicit expressions of these measures and define a new Fisher-Shannon information plane. Performance of the proposed methodology is illustrated by numerical results and applications to condition factor time series.