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The confidence interval of q-Gaussian distributions

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  • Ben Salah Nahla
  • Masmoudi Afif

Abstract

The q-Gaussian is a probability distribution generalizing the Gaussian one. In spite of a q-normal distribution is popular, there is a problem when calculating an expectation value with a corresponding normalized distribution and not a q-normal distribution itself. In this article, two q-moment types called normalized and unnormalized q-moments are introduced in details. Some properties of q-moments are given, and several relationships between them are established, and some results related to q-moments are also obtained. Moreover, we show that these new q-moments may be regarded as a generelazation of the classical case for q = 1. Firstly, we determine the q-moments of q-Gaussian distribution. Especially, we give explicitly the kurtosis parameters. Secondly, we compute the expression of the q-Laplace transform of the q-Gaussian distribution. Finally, we study the distribution of sum of q-independent Gaussian distributions. Afterwards the confidence interval of the mean parameter is estimated on the basis of the q-central limit theorem.

Suggested Citation

  • Ben Salah Nahla & Masmoudi Afif, 2023. "The confidence interval of q-Gaussian distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(10), pages 3511-3525, May.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:10:p:3511-3525
    DOI: 10.1080/03610926.2021.1974482
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