Related papers: Maximum Likelihood Estimation for q-Exponential (T…
Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined…
Recently, we demonstrated the existence of nonextensivity in neuromuscular transmission [Phys. Rev. E 84, 041925 (2011)]. In the present letter, we propose a general criterion based on the q-calculus foundations and nonextensive statistics…
Topp-Leone distribution is a continuous model distribution used for modelling lifetime phenomena. The main purpose of this paper is to introduce a new framework for generating lifetime distributions, called the Topp-Leone generated…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
We investigate a two-parameter entropy introduced by Schw\"{a}mmle and Tsallis and obtain its probability distribution in the canonical ensemble. The probability distribution is given in terms of the Lambert W-function which has been used…
We have obtained the Tsallis distribution from the maximum entropy approach using constraints on the first and the second moment, together with the normalization condition. We have constructed railway and highway communication networks for…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of…
Tsallis' pioneer q-probability distribution $P_i=\frac {[1+\beta(1-q)U_i]^{\frac {1} {q-1}}} {Z}$, $Z=\sum\limits_{i=1}^n [1+\beta(1-q)U_i]^{\frac {1} {q-1}}$ [J. of Stat. Phys., {\bf 52} (1988) 479] has been recently attacked in…
Topp Leone q Exponential Distruibution is a continuous model distribution used for modelling lifetime phenomena. In this study, we introduce different estimation methods for the unknown parameters of Topp Leone Exponential(TLE) distribution…
One of the most common anticipated difficulties in applying mainstream maximum likelihood inference upon extreme values is articulated on the scarcity of extreme observations for bringing the extreme value theorem to hold across a series of…
Recently attention has been drawn to practical problems with the use of unbounded Pareto distributions, for instance when there are natural upper bounds that truncate the probability tail. Aban, Meerschaert and Panorska (2006) derived the…
The Tsallis distribution has been used widely in high energy physics to describe the transverse momnetum distributions of particles. In this note we show that the use of a thermodynamically consistent form of this distribution leads to a…
Quasi-power law ensembles are discussed from the perspective of nonextensive Tsallis distributions characterized by a nonextensive parameter $q$. A number of possible sources of such distributions are presented in more detail. It is further…