The Generalized Omega Function and Its Connection with Some Probability Distributions

Abstract

AbstractIn this paper, we present a generator function-based mapping called the generalized omega function. We show that a particular class of exponential functions is the asymptotic generalized omega function class. Owing to this property of the new function, it can be utilized for constructing bounded alternatives to cumulative distribution functions and density functions of some well-known random variables, including the Weibull, exponential and standard normal.