Contributions to the Weighted Non-Central Chi-Square Distribution
A.Elsherpiny, E., A.Ibrahim, S., Y.Abdelall, Y. (2012). Contributions to the Weighted Non-Central Chi-Square Distribution. EKB Journal Management System, 56(1), 25-37. doi: 10.21608/esju.2012.314326
Elsayed A.Elsherpiny; Sahar A.Ibrahim; Yassmen Y.Abdelall. "Contributions to the Weighted Non-Central Chi-Square Distribution". EKB Journal Management System, 56, 1, 2012, 25-37. doi: 10.21608/esju.2012.314326
A.Elsherpiny, E., A.Ibrahim, S., Y.Abdelall, Y. (2012). 'Contributions to the Weighted Non-Central Chi-Square Distribution', EKB Journal Management System, 56(1), pp. 25-37. doi: 10.21608/esju.2012.314326
A.Elsherpiny, E., A.Ibrahim, S., Y.Abdelall, Y. Contributions to the Weighted Non-Central Chi-Square Distribution. EKB Journal Management System, 2012; 56(1): 25-37. doi: 10.21608/esju.2012.314326

Contributions to the Weighted Non-Central Chi-Square Distribution

The Egyptian Statistical Journal
Article 3, Volume 56, Issue 1, June 2012, Pages 25-37    PDF (5.92 M)
Document Type: Original Article
DOI: 10.21608/esju.2012.314326
Authors
Elsayed A.Elsherpiny* ; Sahar A.Ibrahim; Yassmen Y.Abdelall
Institute f Statistical Studies and Research, Cairo University, Egypt.
Abstract
In this paper, we consider the probability density function (pdf) of the weighted non-central chi-
square distribution with degrees of freedom. This pdf is presented in the literature as an infinite
sum. Consequently we give another expression for this pdf in terms of a generalized
hypergeometric function, modified Bessel function, and hyperbolic cosine function. Also, the
moment is obtained. In addition, we give two alternative expressions to the part of the pdf of the
even terms with odd number of degrees of freedom . Kettani's results (2006) can be obtained as a
special case of our results.
Keywords
Weighted Non; Central Chi; Square Distribution; Modified Bessel Function; Hypergeometric Function
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