A note on explicit expressions for moments of order statistics

• Fredy Castellares ^[1] ; Artur J. Lemonte ^[2] ; Marcos A.C. Santos ^[1]
  1. [1] Universidade Federal de Minas Gerais

     Universidade Federal de Minas Gerais

     Brasil

     
  2. [2] Universidade Federal do Rio Grande do Norte

     Universidade Federal do Rio Grande do Norte

     Brasil

     
• Localización: Spanish journal of statistics, ISSN-e 2695-9070, Nº. 3, 2021, págs. 45-53
• Idioma: inglés
• DOI: 10.37830/SJS.2021.1.04
• Enlaces
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• Resumen

  • Closed-form expressions for moments of order statistics from the normal, log-normal, gamma and beta distributions were provided in the statistics literature. In particular, the explicit expressions involve the Lauricella function of type A, and the generalized Kampé de Fériet function.

    We note that the expressions provided by the author do not appear correct, which implies that the expressions cannot be recommended to users. An alternative closed-form expression for moments of order statistics is then provided. We also consider numerical studies to show that the formulas we provide deliver satisfactory results.