Application of Ujlayan-Dixit Fractional Gamma with Two-Parameters Probability Distribution

Iqbal H. Jebril; Iqbal M. Batiha; Nadia Allouch

doi:10.19139/soic-2310-5070-2591

Application of Ujlayan-Dixit Fractional Gamma with Two-Parameters Probability Distribution

Iqbal H. Jebril
, Iqbal M. Batiha
, Nadia Allouch

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
University of Mostaganem

Research output: Contribution to journal › Article › peer-review

Abstract

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, r^th-moments, r^th-central moments, variance and standard deviation. Finally, the UD fractional entropy measures, such as Shannon, Tsallis, and Rényi entropy, are explained.

Original language	English
Pages (from-to)	2104-2117
Number of pages	14
Journal	Statistics, Optimization and Information Computing
Volume	14
Issue number	4
DOIs	https://doi.org/10.19139/soic-2310-5070-2591
State	Published - 26 Sep 2025

Keywords

Continuous random variables
Entropy
Gamma with two parameters distribution
Probability distribution
UD fractional derivative

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10.19139/soic-2310-5070-2591

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abstract = "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{\'e}nyi entropy, are explained.",

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AU - Jebril, Iqbal H.

AU - Batiha, Iqbal M.

AU - Allouch, Nadia

PY - 2025/9/26

Y1 - 2025/9/26

N2 - 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 Rényi entropy, are explained.

AB - 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 Rényi entropy, are explained.

KW - Continuous random variables

KW - Entropy

KW - Gamma with two parameters distribution

KW - Probability distribution

KW - UD fractional derivative

UR - https://www.scopus.com/pages/publications/105017243203

U2 - 10.19139/soic-2310-5070-2591

DO - 10.19139/soic-2310-5070-2591

M3 - Article

AN - SCOPUS:105017243203

SN - 2311-004X

VL - 14

SP - 2104

EP - 2117

JO - Statistics, Optimization and Information Computing

JF - Statistics, Optimization and Information Computing

IS - 4

ER -

Application of Ujlayan-Dixit Fractional Gamma with Two-Parameters Probability Distribution

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Keywords

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