Physica A 285 (2000) 547–565 www.elsevier.com/locate/physa Recognition of nonextensive statistical distributions by the eigencoordinates method R.R. Nigmatullin ∗ Theoretical Physics Department, Kazan State University, Kazan, 420008, Tatarstan, Russia Received 22 December 1999; received in revised form 2 February 2000 Abstract Nonextensive statistical distributions suggested by Tsallis are studied in the framework of the so-called eigencoordinates (ECs) method which allows to recognize them with high level of authenticity. At rst, the possibilities of the ECs method have been demonstrated on model les to exhibit some peculiarities of this new method. Then the amplitude distributions of the real noise tracks before and after earthquakes have been analyzed. It has been shown that this type of noise is fractal and strongly correlated; histograms of the noise amplitudes with high level of reliability are really described by a distribution coming from nonextensive statistics. The possibilities and recommendations for the application of the ECs method to identify theoretical curves claimed for the description of experimental data are discussed. c 2000 Elsevier Science B.V. All rights reserved. PACS: 02.60.Ed, Pn; 06.20.Dk; 07.05.Kf, Rm Keywords: Nonextensive statistics; Nonextensive distribution functions; Eigen-Coordinates Method; Fractal noises; Earthquake noise 1. Introduction In the review [1] the basic principles of nonextensive statistics have been discussed. An important conclusion which follows from the generalized denition of entropy [2] is the existence of new type of distributions which can play a decisive role in justication of new statistical mechanics. These distributions can be expressed in * Corresponding author; Present address: Department of Physics, University of Jordan, Amman, Jordan. E-mail addresses: raoul.nigmatullin@ksu.ru, raoul@psuct.edu.jo, raoul@sci.ju.edu.jo (R.R. Nigmatullin). 0378-4371/00/$ - see front matter c 2000 Elsevier Science B.V. All rights reserved. PII: S0378-4371(00)00237-5