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A Simple Representation of the Weighted Non-Central Chi-Square Distribution

Dr. Elsayed A. Elsherpieny ,Dr. Sahar A. Ibrahim, Dr. Yassmen, Y. Abdelall

In this paper we consider the probability density function (pdf) of the weighted non-central chi-square distribution with  degrees of freedom. This pdf presented in the literature as an infinite sum. Herein, we present an alternative simple expression to this pdf which may be useful in the future studies. The results of Kettani (2006) and Andras and Baricz (2008) can be obtained as a special case from ours.