Detecting q-Gaussian distributions and the normalization effect

TL;DR

This paper demonstrates that normalization preprocessing can cause data with elliptical symmetry to appear as q-Gaussian distributions, highlighting the importance of careful interpretation in distribution detection.

Contribution

It reveals that normalization can induce q-Gaussian appearances in data and provides a method to deduce the q parameter from the normalization process.

Findings

Normalized data with elliptical symmetry appear as q-Gaussian distributions.

Gaussian data can be mistaken for q-Gaussian after normalization.

The q parameter can be inferred from the normalization technique.

Abstract

We show that whenever data are gathered using a device that performs a normalization-preprocessing, the ensuing normalized input, as recorded by the measurement device, will always be q-Gaussian distributed if the incoming data exhibit elliptical symmetry. As a consequence, great care should be exercised when detecting q-Gaussians. As an example, Gaussian data will appear, after normalization, in the guise of q-Gaussian records. Moreover, we show that the value of the resulting parameter q can be deduced from the normalization technique that characterizes the device.