TL;DR
This paper introduces a new formula that expresses cumulants as iterated integrals of the distribution function, extending previous results for cumulants up to order 4.
Contribution
It generalizes existing formulas by providing a comprehensive iterated integral representation for cumulants of any order.
Findings
Derived a general formula for cumulants as iterated integrals
Extended previous results to higher-order cumulants
Provides a new tool for analyzing distribution properties
Abstract
A formula expressing cumulants in terms of iterated integrals of the distribution function is derived. It generalizes results of Jones and Balakrishnan who computed expressions for cumulants up to order 4.
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