Search results
Results from the WOW.Com Content Network
This distribution is a common alternative to the asymptotic power-law distribution because it naturally captures finite-size effects. The Tweedie distributions are a family of statistical models characterized by closure under additive and reproductive convolution as well as under scale transformation. Consequently, these models all express a ...
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically.That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as
In the long run, exponential growth of any kind will overtake linear growth of any kind (that is the basis of the Malthusian catastrophe) as well as any polynomial growth, that is, for all α: = There is a whole hierarchy of conceivable growth rates that are slower than exponential and faster than linear (in the long run).
The Pareto distribution, or "power law" distribution, used in the analysis of financial data and critical behavior. The Pearson Type III distribution; The phase-type distribution, used in queueing theory; The phased bi-exponential distribution is commonly used in pharmacokinetics; The phased bi-Weibull distribution
Above , (, =) exhibits a combined exponential and power-law dependence on distance: (, =) / (). The power-law dependence dominates at distances short relative to the correlation length, ξ {\displaystyle \xi } , while the exponential dependence dominates at distances large relative to ξ {\displaystyle \xi } .
The distribution of the vertex degrees of a BA graph with 200000 nodes and 2 new edges per step. Plotted in log-log scale. It follows a power law with exponent -2.78. The degree distribution resulting from the BA model is scale free, in particular, it is a power law of the form ()
In other words, the preferential attachment process generates a "long-tailed" distribution following a Pareto distribution or power law in its tail. This is the primary reason for the historical interest in preferential attachment: the species distribution and many other phenomena are observed empirically to follow power laws and the ...
With binary data, the random distribution is the binomial (not the Poisson). Thus the Taylor power law and the binary power law are two special cases of a general power-law relationships for heterogeneity. When both a and b are equal to 1, then a small-scale random spatial pattern is suggested and is best described by the binomial distribution.