Theoretical L-moments and TL-moments Using Combinatorial Identities and Finite Operators

Christophe Dutang (1)

1 LMM - Laboratoire Manceau de Mathématiques

Moments have been traditionally used to characterize a probability distribution. Recently, L-moments and trimmed L-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.

Mots clés: L-moments; Trimmed L-moments; Combinatorial identities; Finite-element operators; Uni-form distribution; Exponential distribution

Domaines: Statistiques [math.ST]

Christophe Dutang. Theoretical L-moments and TL-moments Using Combinatorial Identities and Finite Operators. 2015. ⟨hal-01163638v1⟩