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. © 2002 Hindawi Publishing Corporation. All rights reserved.
Nakhi, Y. B., & Kalla, S. L. (2002). A generalized beta function and associated probability density. International Journal of Mathematics and Mathematical Sciences, 30(8), 467–478. https://doi.org/10.1155/S0161171202007512