Journal of Applied Mathematics and Decision Sciences
Volume 2005 (2005), Issue 4, Pages 191-199

On the ratio of Pearson type VII and Bessel random variables

Saralees Nadarajah1 and Samuel Kotz2

1Department of Statistics, University of Nebraska, Lincoln 68583, NE, USA
2Department of Engineering Management and Systems Engineering, George Washington University, Washington 20052, DC, USA

Received 26 October 2004

Copyright © 2005 Saralees Nadarajah and Samuel Kotz. 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 exact distribution of the ratio |X/Y| is derived when X and Y are, respectively, Pearson type VII and Bessel function random variables distributed independently of each other. The work is motivated by previously published approximate relationships between these two distributions. An application of the result is provided by computing “correction factors” for some of these approximations.