Random populations represented by stochastically scattered collections of real-valued points are abundant across many fields of science. Fractality, in the context of random populations, is conventionally associated with a Paretian distribution of the population's values.

A theory which describes the share price evolution at financial markets as a continuous-time random walk (Physica A 287 (2000) 468, Physica A 314 (2002) 749, Eur. Phys. J. B 27 (2002) 273, Physica A 376 (2000) 284) has been generalized in order to take into account the dependence of waiting...

We investigate two coupled properties of Lévy stable random motions: the first passage times (FPTs) and the first passage leapovers (FPLs). While, in general, the FPT problem has been studied quite extensively, the FPL problem has hardly attracted any attention. Considering a particle that...

We consider a non-additive generalization of the Shannon entropy measure using order statistics and show that this entropy measure characterizes the distribution function uniquely. Further we propose a residual non-additive entropy measure for order statistics and prove a characterization result...

We investigate the behavior of the Shannon entropy, S(T), and the time generalized q-entropy, Sq(T), at increasing aggregation intervals, T, using series of 15-min and hourly rainfall records in the tropical Andes of Colombia, spanning from 21 months to 40 years, as well as average daily...

We calculate the time-dependent Shannon (Sx and Sp) entropy and Fisher (Fx and Fp) information of three log-periodic oscillators. We obtain a general expression for Sx,p and Fx,p in the state n=0 in terms of ρ, a c-number quantity satisfying a nonlinear differential equation. For two out of...

The time dynamics of seismic microtremors recorded in several sites in Chisinau City (Moldova) are analysed by means of the informational approaches of the Fisher Information Measure (FIM) and the Shannon entropy. The sites show different soil characteristics. One of the investigated sites,...

A measure of redundancy inherent in the layouts of water distribution networks is developed using the Tsallis entropy. Both the local redundancy at a node and the global redundancy due to the redundancies at adjacent nodes are derived. The redundancy measure is applied to layouts reported in the...

We calculate the Shannon entropy of a time series by using the probability density functions of the characteristic sizes of the long-range correlated clusters introduced in [A. Carbone, G. Castelli, H.E. Stanley, Phys. Rev. E 69 (2004) 026105]. We define three different measures of the entropy...

Fourth order moments and their connection with other statistics, including second order moments, skewness and entropy, in stable boundary layers are investigated with a large eddy simulation model (LES), wind tunnel experiment data (WT) and measurements on a meteorological tower in an urban area...