Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions

Scaling in cognitive performance reflects multiplicative multifractal cascade dynamics

Self-organized criticality purports to build multi-scaled structures out of local interactions. Evidence of scaling in various domains of biology may be more generally understood to reflect multiplicative interactions weaving together many disparate scales. The self-similarity of power-law scaling entails homogeneity: fluctuations distribute themselves similarly across many spatial and temporal...

Multiplier phenomenology in random multiplicative cascade processes

We demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artifact of the observation procedure. Taking the latter into account, all reported properties of both unconditioned and conditioned multiplier distributions can be reproduced by cascade models with uncorrelated random ...

GENERALIZED BINOMIAL AND NEGATIVE BINOMIAL DISTRIBUTIONS OF ORDER k BY THE/-OVERLAPPING ENUMERATION SCHEME

A b s t r a c t . In this paper, we investigate the exact distribution of the waiting time for the r-th t-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of order k and an extended Poisson distr...

Multiplicity Distributions in Strong Interactions: a Generalized Negative Binomial Model

A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in totaland limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of the KNO scaling function derived in Polyakov’s similarity hypothesis for strong interactions as well as in perturbative QCD, ψ(z) ∝ zα exp(−zμ). Various chara...

Binomial and multinomial distributions