Some properties of q-Gaussian distributions
In: ISSN: 0361-0926, 2023
academicJournal
Zugriff:
International audience ; In this research article, we introduced the notion of q-probabilty distributions in quantum calculus. We characterized the concept of q-density by connecting it to a probability measure and investigated some of their outstanding properties. In this case, the Transfer theorem was extended in order to compute afterwards the q-moments, q-entropy, q-moment generating function, and q-quantiles. We are also interested in finding the centered q-Gaussian distribution Nq (0,σ2) with variance σ2. We also proved that this q-distribution belongs to a class of classical discrete distributions. The centered q-Gaussian law Nq (0,σ2) is also naturally related to the q-Gaussian distribution Nq(μ,σ2) with mean μ and standard deviation σ. We corroborated that the q-moments of these q-distributions are q-analogs of the moments of classical distributions. Numerical studies demonstrated that Nq (0,σ2) interpolates between the classical Uniform and Gaussian distributions when q goes to 0 and 1, respectively. Subsequently, simulation studies for various q parameter values and samples sizes of the Gaussian q-distributions were conducted to demonstrate the effectiveness of the proposed model. Eventually, we provided some pertinent closing remarks and offered new perspectives for future works.
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Some properties of q-Gaussian distributions
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Autor/in / Beteiligte Person: | Oumaima, Ben Mrad ; Masmoudi, Afif ; Slaoui, Yousri ; Laboratory of Probability and Statistics ; Faculté des Sciences de Sfax (FSS) ; Université de Sfax - University of Sfax-Université de Sfax - University of Sfax ; Laboratoire de mathématiques et applications UMR 7348 (LMA Poitiers ) ; Université de Poitiers = University of Poitiers (UP)-Centre National de la Recherche Scientifique (CNRS) ; Hubert Curien “PHC-Utique” program (CMCU number: 20G1503–Campus France number: 44172SL) ; Project CPER “E-Data” funded by the Région Nouvelle-Aquitaine ; Programme opérationnel FEDER/FSE 2014-2020 funded by Région Nouvelle-Aquitaine and the European Union |
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Zeitschrift: | ISSN: 0361-0926, 2023 |
Veröffentlichung: | HAL CCSD ; Taylor & Francis, 2023 |
Medientyp: | academicJournal |
DOI: | 10.1080/03610926.2023.2244097 |
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