International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 18, Pages 2977-2989

On the product and ratio of Bessel random variables

Saralees Nadarajah1 and Arjun K. Gupta2

1Department of Statistics, College of Arts and Sciences, University of Nebraska, Lincoln 68583-0712, NE, USA
2Department of Mathematics and Statistics, College of Arts and Sciences, Bowling Green State University, Bowling Green 43403-0221, OH, USA

Received 20 January 2005

Copyright © 2005 Saralees Nadarajah and Arjun K. Gupta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.