Application of Ujlayan-Dixit (UD) Fractional Gamma With Two-Parameters Probability Distribution - Jebril, Iqbal H.; Batiha, Iqbal; Allouch, Nadia (Statistics, Optimization & Information Computing, 2025)
The main goal in this research is to use the Ujlayan-Dixit (UD) fractional derivative to generate a new fractional probability density function for the two-parameters gamma distribution, and develop some applications of this new distribution like cumulative distribution, survival and hazard functions. Additionally, we will establish other concepts and applications for continuous random variables by applying the UD fractional analogues of statistical measures including expectation, rth-moments, rth-central moments, variance and standard deviation. Finally, the UD fractional entropy measures, such as Shannon, Tsallis, and R´enyi entropy, are explained.