Related papers: First-Digit Law in Nonextensive Statistics
A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysical under specific…
In many real life situations, it is observed that the first digits (i.e., $1,2,\ldots,9$) of a numerical data-set, which is expressed using decimal system, do not follow a random distribution. Instead, smaller numbers are favoured by nature…
Benford's law predicts the occurrence of the $n^{\mathrm{th}}$ digit of numbers in datasets originating from various sources of the world, ranging from financial data to atomic spectra. It is intriguing that although many features of…
In this paper, we will see that the proportion of d as leading digit, d $\in$ 1, 9, in data (obtained thanks to the hereunder developed model) is more likely to follow a law whose probability distribution is determined by a specific upper…
Fix a base B and let zeta have the standard exponential distribution; the distribution of digits of zeta base B is known to be very close to Benford's Law. If there exists a C such that the distribution of digits of C times the elements of…
Recently we have demostrated that the nonextensitivity parameter q occuring in some applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is, in the q>1 case, given entirely by the fluctuations of…
Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits $q$-exponential or power law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we…
During the past few years, nonextensive statistics has been successfully applied to explain many different kinds of systems. Through these studies some interpretations of the entropic parameter q, which has major role in this statistics, in…
Nature and our world have a bias! Roughly $30\%$ of the time the number $1$ occurs as the leading digit in many datasets base $10$. This phenomenon is known as Benford's law and it arrises in diverse fields such as the stock market,…
Iafrate, Miller, and Strauch [Equipartition and a Distribution for Numbers: A Statistical Model for Benford's Law," arXiv:1503.08259] construct and test a statistical model for partitioning a conserved quantity. One consequence of their…
Considering the first significant digits (noted d) in data sets of dissipation for turbulent flows, the probability to find a given number (d=1 or 2 or... 9) would be 1/9 for an uniform distribution. Instead the probability closely follows…
Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like…
A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to…
Benford's law is a famous law in statistics which states that the leading digits of random variables in diverse data sets appear not uniformly from 1 to 9; the probability that d (d=1,...,9) appears as a leading digit is given by…
In order to improve the teaching of the course of statistical physics in universities, in this article we introduce nonextensive statistics, a new statistical theory about complex systems. We study the two modification coefficients a and b…
Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently…
The uneven distribution of digits in numerical data, known as Benford's law, was discovered in 1881. Since then, this law has been shown to be correct in copious numerical data relating to economics, physics and even prime numbers. Although…
The nonextensitivity parameter $q$ occuring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in $q>1$ case, entirely by the fluctuations of the parameters…
The renowned proverb, Numbers do not lie, underscores the reliability and insight that lie beneath numbers, a concept of undisputed importance, especially in economics and finance etc. Despite the prosperity of Benford's Law in the first…
The probability that a number in many naturally occurring tables of numerical data has first significant digit $d$ is predicted by Benford's Law ${\rm Prob} (d) = \log_{10} (1 + {\displaystyle{1\over d}}), d = 1, 2 >..., 9$. Illustrations…