On a logarithmic integral and the moments of order statistics from the Weibull-geometric and half-logistic families of distributions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Jodra, P.¹  Jimenez-Gamero, M. D.² 

[1] Univ Zaragoza, Dpto Metodos Estadist, Zaragoza 50018, Spain

[2] Univ Seville, Dpto Estadist & Invest Operat, E-41012 Seville, Spain

关键词: Polylogarithm function;    Stirling numbers;    Weibull-geometric distribution;    Half-logistic distribution;    Order statistics;    Moments;   

DOI  :  10.1016/j.jmaa.2013.09.001

来源: Elsevier

【 摘 要 】

We provide an explicit analytical solution for a logarithmic integral in terms of the Lerch transcendent function together with the generalized Stirling numbers of the first kind. For some special cases of interest in statistical applications, the explicit solution can be expressed in terms of the polylogarithm function together with the aforementioned Stirling numbers. As a consequence, we obtain explicit expressions for the moments of order statistics from the half-logistic distribution, the Weibull-geometric distribution and the long-term Weibull-geometric distribution, which include as particular cases the extended exponential-geometric distribution and the long-term extended exponential-geometric distribution, among others. These analytical expressions are useful for computational purposes. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free