Inequalities for m-Divisible Distributions and Testing of Infinite Divisibility
Lev B. Klebanov, Ashot V. Kakosyan, Irina V. Volchenkova
TL;DR
This paper introduces inequalities related to m-divisible and infinitely divisible distributions and proposes a statistical test to determine if a distribution is infinitely divisible, based on these inequalities.
Contribution
The paper presents new inequalities for m-divisible and infinitely divisible characteristic functions and develops a statistical test for infinite divisibility.
Findings
Derived inequalities for characteristic functions.
Proposed a statistical test for infinite divisibility.
Validated the test's effectiveness.
Abstract
We state some inequalities for m-divisible and infinite divisible characteristic functions. Basing on them we propose a statistical test for a distribution to be infinitely divisible. Keywords: infinite divisible distributions; statistical tests.
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Taxonomy
TopicsMathematical Approximation and Integration · Approximation Theory and Sequence Spaces · Advanced Statistical Process Monitoring