Hellinger’s Distance and Correlation for a Subclass of Stable Distributions
Mesrop Mesropyan, V. G. Bardakhchyan · Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) · 2023
We investigated correlation retrieval procedure from Hellinger’s distance. We found monotone relation of Hellinger’s distance and positive correlation in a subclass of stable distributed random variables, with $$\alpha>1$$ and $$\mu=\beta=0$$ . We implemented a technique suitable for the class of stable distributions, and showed that this positive relation holds even for the case of Levy distribution, i.e., $$\alpha=1/2$$ , $$\beta=1$$ , and $$\mu=0$$ .