Application of Ujlayan-Dixit Fractional Exponential Probability Distribution - Iqbal H. Jebril; Raed Hatamleh; Iqbal Batiha; Nadia Allouch (Statistics, Optimization & Information Computing, 2025)
This research aims to present the probability density functions of random variables for exponential distribution by applying a new technique of the Ujlayan-Dixit (UD) fractionalde rivative and to find some basic concepts related to probability distributions of random variables, which are density, cumulative distribution, survival, and hazard functions. In addition, we provide the UD fractional isotopes with the expected values, rth moments, rth central moments, mean, variace, skewness, and kurtosis. Finally, we give the UD fractional analogs to some entropy measures such as Shannon, Renyi, and Tsallis entropy.