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.