Almost Sure Local Limit Theorem for the Dickman distribution
Rita Giuliano, Zbigniew Szewczak, Michel Weber
TL;DR
This paper establishes an Almost Sure Local Limit Theorem for the Dickman distribution using a novel correlation inequality, advancing understanding of the distribution's probabilistic properties.
Contribution
It introduces a new correlation inequality and applies it to prove an Almost Sure Local Limit Theorem for the Dickman distribution, a novel result in probability theory.
Findings
Proved an Almost Sure Local Limit Theorem for the Dickman distribution.
Developed a new correlation inequality applicable to the Dickman distribution.
Extended the theoretical understanding of the Dickman distribution's probabilistic behavior.
Abstract
In this paper we present a new correlation inequality and use it for proving an Almost Sure Local Limit Theorem for the so-called Dickman distribution. Several related results are also proved
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Taxonomy
TopicsStatistical Distribution Estimation and Applications · Probability and Risk Models · Mathematical Inequalities and Applications