Theoretical L-moments and TL-moments using combinatorial identities and finite operators

Christophe Dutang

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 8, 3801-3828

Abstract: Moments have been traditionally used to characterize a probability distribution. Recently, linear moments (L-moments) and trimmed L-moments (TL-moments) are appealing alternatives to the conventional moments. This paper focuses on the computation of theoretical L-moments and TL-moments and emphasizes the use of combinatorial identities. We are able to derive new closed-form formulas of L-moments and TL-moments for continuous probability distributions. Finally, closed-form formulas for the L-moments for the exponential distribution and the uniform distribution are also obtained.

Date: 2017
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DOI: 10.1080/03610926.2015.1073313

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