Some properties of q-Gaussian distributions - Université de Poitiers Accéder directement au contenu
Article Dans Une Revue Communications in Statistics - Theory and Methods Année : 2023

Some properties of q-Gaussian distributions

Résumé

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.
Fichier non déposé

Dates et versions

hal-04389482 , version 1 (11-01-2024)

Identifiants

Citer

Ben Mrad Oumaima, Afif Masmoudi, Yousri Slaoui. Some properties of q-Gaussian distributions. Communications in Statistics - Theory and Methods, 2023, pp.1-23. ⟨10.1080/03610926.2023.2244097⟩. ⟨hal-04389482⟩
19 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More