Extended Exponential Distribution With Application On Financial Data

In this paper, we present a novel approach to extend the applicability of probability density functions (PDFs) for the exponential distribution, enabling the creation of a versatile family of PDFs with diverse properties. Our method utilizes fundamental statistical parameters, such as the rate parameter, to facilitate this expansion. The central contribution of this research is the development and proof of a powerful Generalization Theorem for Exponential PDFs. This theorem allows for the nth-generation generalization of exponential PDFs, each iteration introducing unique characteristics. We apply our Generalization Theorem specifically to exponential PDFs, displaying its wide-ranging utility within this domain. Additionally, we conduct estimation and simulation studies to assess the performance of the generalized exponential PDFs in comparison to their original counterparts. We hereby christen this groundbreaking theorem as the ?Exponential PDF Generalization Theorem.? This paper marks a significant advancement in the manipulation and adaptation of exponential probability density functions, ushering in new avenues for statistical modeling and analysis within the realm of exponential distributions.