International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 8, Pages 467-478
doi:10.1155/S0161171202007512
A generalized beta function and associated probability density
Kuwait University, Department of Mathematics and Computer Science, P.O. Box 5969, Safat 13060, Kuwait
Received 30 April 2001
Copyright © 2002 Y. Ben Nakhi and S. L. Kalla. 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.
Abstract
We introduce and establish some properties of a generalized form
of the beta function. Corresponding generalized incomplete beta
functions are also defined. Moreover, we define a new probability
density function (pdf) involving this new generalized beta
function. Some basic functions associated with the pdf, such as
moment generating function, mean residue function, and hazard rate
function are derived. Some special cases are mentioned. Some
figures for pdf, hazard rate function, and mean residue life
function are given. These figures reflect the role of shape and
scale parameters.