A fractal (power-law) distribution is the only statistical distribution applicable to a scale-invariant process. One of the major problems in petrology is the distribution of trace elements in the Earth’s crust. Extreme values of this distribution result in ore deposits. There is accumulating observational evidence that tonnage–grade statistics of ore deposits are often fractal (powerlaw). Rayl...

A computational model of loose snow avalanches was studied as an example of Self-Organized Criticality (SOC). The distribution of the magnitudes of avalanches was measured for a stairstepped system with various critical relative differences and system slopes. Depending on the configuration, the model showed either power law behaviors or a Gaussian distribution. For configurations that displayed...

The Generalized Lotka Voltera (GLV) formalism has been introduced in order to explain the power law distributions in the individual wealth (wi(t)) (Pareto law) and financial markets returns (fluctuations) (r) as a result of the auto-catalytic (multiplicative random) character of the individual capital dynamics. As long as the multiplicative random factor (λ) is extracted from the same probabili...

In this paper we will show that, the non-Gaussian statistics framework based on the Kaniadakis statistics is more appropriate to fit the observed distributions of projected rotational velocity measurements of stars in the Pleiades open cluster. To this end, we compare the results from the κ and q-distributions with the Maxwellian. Copyright c © EPLA, 2008 Introduction. – Some restrictions to th...

To be published in Phys. Rev. E (2005). We present a simple point process model of 1/f β noise, covering different values of the exponent β. The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some interv...

We present a simple point process model of 1/f(beta) noise, covering different values of the exponent beta . The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence, or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some interval resulting in a power-law dis...

Many scientists are interested in but puzzled by the various inverse power laws with a negative exponent 1 such as the rank-size rule. The rank-size rule is a very simple scaling law followed by many observations of the ubiquitous empirical patterns in physical and social systems. Where there is a rank-size distribution, there will be a hierarchy with cascade structure. However, the equivalence...

In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains the bivariate generalized exponential-Poisson, bivariate generalized exponential-logarithmic, bivariate generalized exponential-binomial and bivariate generalized exponential-negative binomial distributions as specia...

We examine avalanche statistics of rainand vibrationdriven granular slides in miniature soil mounds using experimental and numerical approaches. A crossover from powerlaw to non power-law avalanche-size statistics is demonstrated as a generic driving rate ν is increased, due to diminishing timescale separation (∼ ν) between stress buildup and release. For slowly-driven mounds, the tail of the a...