Hellinger’s distance and correlation for a subclass of stable distributions. (English) Zbl 1526.60017
J. Contemp. Math. Anal., Armen. Acad. Sci. 58, No. 3, 191-195 (2023) and Izv. Nats. Akad. Nauk Armen., Mat. 58, No. 3, 78-83 (2023).
Summary: 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 \(\mu=0\).
MSC:
| 60E07 | Infinitely divisible distributions; stable distributions |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
References:
| [1] | S. T. Rachev, L. Klebanov, S. V. Stoyanov, and F. Fabozzi, The Methods of Distances in the Theory of Probability and Statistics (Springer, New York, 2013). https://doi.org/10.1007/978-1-4614-4869-3 · Zbl 1280.60005 |
| [2] | Aap. Hyvárinen, J. Karhunen, and Er. Oja, Independent Component Analysis (Wiley, Newark, N.J., 2001). |
| [3] | Mesropyan, M.; Mkrtchyan, V., Assessing normality of group of assets based on portfolio construction, Alternative, 3, 14-21 (2021) |
| [4] | K.-J. Miescke and F. Liese, Statistical Decision Theory: Estimation, Testing, and Selection, Springer Series in Statistics (Springer, New York, 2008). https://doi.org/10.1007/978-0-387-73194-0 · Zbl 1154.62008 |
| [5] | Linde, W., Probability in Banach Spaces: Stable and Infinitely Divisible Distributions (1986) · Zbl 0665.60005 |
| [6] | F. Nielsen and K. Okamura, ‘‘On f-divergences between Cauchy distributions,’’ IEEE Trans. Inf. Theory (2022). https://doi.org/10.1109/TIT.2022.3231645 · Zbl 07495281 |
| [7] | L. Debnath and D. Bhatta, Integral Transforms and Their Applications (Chapman & Hall/CRC, 2007). https://doi.org/10.1201/b17670 · Zbl 1310.44001 |
| [8] | Gerber, H. U., A characterization of certain families of distributions via Esscher transforms and independence, J. Am. Stat. Assoc., 75, 1015-1018 (1980) · Zbl 0448.62007 · doi:10.1080/01621459.1980.10477589 |
| [9] | J.-Ph. Aguilar, C. Coste, H. Kleinert, and J. Korbe, ‘‘Regularization and analytic option pricing under \(\alpha \)-stable distribution of arbitrary asymmetry,’’ (2016). arXiv:1611.04320 [q-fin.PR] |
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