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

Domaines: Statistiques [math.ST]

Christophe Dutang. Theoretical L-moments and TL-moments Using Combinatorial Identities and Finite Operators. Communications in Statistics - Theory and Methods, 2017, 46 (8), pp.3801-3828. ⟨10.1080/03610926.2015.1073313⟩. ⟨hal-01163638v2⟩