Generating novel probability distributions: A UD fractional derivative approach

Abstract

This study introduces novel probability distributions derived from the Dixit and Ujlayan (UD) fractional differential equation. By applying the UD fractional differential equation to established continuous probability distributions, new probability distributions are formulated. The resulting UD fractional probability distributions extend classical distributions such as the gamma, power function, arcsine, and beta distributions, thereby expanding the theoretical framework for probability modeling. An application of the UD fractional Beta distribution to a real-world dataset demonstrates its superior flexibility and adaptability compared to the classical Beta distribution, particularly in modeling skewed and bounded data. These findings underscore the potential of UD fractional distributions in addressing complex data modeling challenges across diverse fields.