The confidence interval of q-Gaussian distributions

Ben Salah Nahla and Masmoudi Afif

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 10, 3511-3525

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.

Date: 2023
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DOI: 10.1080/03610926.2021.1974482

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