In blinking surface-enhanced Raman scattering (SERS), probability distributions of the bright and dark events against their duration times are reproduced by a power-law without and with an exponential function, respectively. The truncation at the tail of the power-law suggests not only a potential well but also an energy barrier during a single molecule optical trapping onto the junction.

We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power laws or for exponentials correspondingly, regardless of the value of the exponent o...

In this paper we tackle the problem of estimating the power-law tail exponent of income distributions by using the Hill’s estimator. A subsample semi-parametric bootstrap procedure minimizing the mean squared error is used to choose the power-law cutoff value optimally. This technique is applied to personal income data for Australia and Italy. r 2006 Elsevier B.V. All rights reserved.

For a large class of statistical systems a geometric mean value of the ob-servables is constrained. These observables are characterized by a power-law statistical distribution. In everyday life we find events of very different nature often to follow similar statistical distributions. These distributions arise because the same stochastic process is at work, and this process can be understood bey...

Recently much attention has been paid to the nonextensive canonical distributions: the αfamilies. Such distributions have been found in many real-world systems such as fully developed turbulence and financial markets. In this paper, a generalized mean-field method to approximate the expectations of the α-families is proposed. We calculate the α′-projection of a probability distribution to find ...

From the available literature, the allometric scaling laws generally exist in biology, ecology, etc. These scaling laws obey power law distributions. A possibly better approach to characterize the power law is to utilize fractional derivatives. In this paper, we establish a fractional differential equation model for this allometry by using the Caputo fractional derivatives.

There has been some confusion concerning the animal group size: an exponential distribution was deduced by maximizing the entropy; lognormal distributions were practically used; as power-law decay with exponent 3/2 was proposed in physical analogy to aerosol condensation. Here I show that the animal group-size distribution follows a power-law decay with exponent 1, and is truncated at a cut-off...

Complex networks have recently aroused a lot of interest. However, network edges are considered to be the same in almost all these studies. In this paper, we present a simple classification method, which divides the edges of undirected, unweighted networks into two types: p2c and p2p. The p2c edge represents a hierarchical relationship between two nodes, while the p2p edge represents an equal r...

We investigate into the rank-size distributions of urban agglomerations for India between 1981 to 2011. The incidence of a power law tail is prominent. A relevant question persists regarding the evolution of the power tail coefficient. We have developed a methodology to meaningfully track the power law coefficient over time, when a country experience population growth. A relevant dynamic law, G...

We develop an abstract model of information acquisition from redundant data. We assume a random sampling process from data which contain information with bias and are interested in the fraction of information we expect to learn as function of (i) the sampled fraction (recall) and (ii) varying bias of information (redundancy distributions). We develop two rules of thumb with varying robustness. ...