The Kummer distribution in free probability, and its characterizations
Marcin \'Swieca
TL;DR
This paper explores the free probability analogue of the Kummer distribution, characterizing free-Kummer and free Poisson distributions using freeness properties, subordination, and Boolean cumulants.
Contribution
It introduces the free Kummer distribution and provides new characterizations based on freeness and conditional moments, expanding free probability theory.
Findings
Characterization of free-Kummer distribution via freeness properties
Identification of conditions for free Poisson distribution
Application of subordination and Boolean cumulants in proofs
Abstract
We study the analogue of Kummer distribution in free probability. We prove characterization of free-Kummer and free Poisson distributions by freeness properties together with some assumptions about conditional moments. Our main tools are subordination of free multiplicative convolution and Boolean cumulants.
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Taxonomy
TopicsStatistical Distribution Estimation and Applications · Probability and Risk Models · Financial Risk and Volatility Modeling