Application of Ujlayan-Dixit Fractional Chi-Square Probability Distribution

Authors

  • Iqbal H. Jebril Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan
  • Raed Hatamleh Department of Mathematics, Jadara University, Irbid 21110, Jordan
  • Iqbal Batiha Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
  • Nadia Allouch Laboratory of pure and applied mathematics, University of Mostaganem, Algeria

DOI:

https://doi.org/10.19139/soic-2310-5070-2334

Keywords:

Chi-Square Distribution (CSD), Continuous Random Variables, Probability Distribution, UD Fractional Derivative, Entropy

Abstract

In this study, we take into account the Ujlayan-Dixit (UD) fractional derivative in order to introduce the fractional probability density function for the Chi-Square distribution (CSD), and to establish certain new applications for this distribution through the use of fractional concepts in probability theory, such as cumulative distribution, survival, and hazard functions. Furthermore, other ideas and applications for continuous random variables are developed using the UD fractional analogs of statistical measures, which are expectation, rth-moments, rth-central moments, variance, and standard deviation. Lastly, we provide the UD fractional entropy measures, including Shannon, Tsallis, and R´enyi entropy.

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Published

2025-06-03

Issue

Vol. 14 No. 1 (2025)

Section

Research Articles

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How to Cite

Application of Ujlayan-Dixit Fractional Chi-Square Probability Distribution. (2025). Statistics, Optimization & Information Computing, 14(1), 373-386. https://doi.org/10.19139/soic-2310-5070-2334