کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4616286 | 1631566 | 2014 | 9 صفحه PDF | دانلود رایگان |
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.
Journal: Journal of Mathematical Analysis and Applications - Volume 410, Issue 2, 15 February 2014, Pages 882–890