Theoretical L-moments and TL-moments using combinatorial identities and finite operators |
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| Authors: | Christophe Dutang |
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| Institution: | Laboratoire Manceau de Mathématique, Université du Maine, Le Mans, France |
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| 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. |
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| Keywords: | Combinatorial identities exponential distribution finite-element operators L-moments trimmed L-moments uniform distribution |
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