Application of Ujlayan-Dixit Fractional Chi-Square Probability Distribution

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 probabil...

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Veröffentlicht in:Statistics, optimization & information computing Jg. 14; H. 1; S. 373 - 386
Hauptverfasser: Jebril, Iqbal H., Hatamleh, Raed, Batiha, Iqbal, Allouch, Nadia
Format: Journal Article
Sprache:Englisch
Veröffentlicht: 20.06.2025
ISSN:2311-004X, 2310-5070
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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.
AbstractList 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.
Author Jebril, Iqbal H.
Batiha, Iqbal
Allouch, Nadia
Hatamleh, Raed
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  surname: Allouch
  fullname: Allouch, Nadia
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