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