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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 ...
There are two major components that explain the emergence of the power-law distribution in the Barabási–Albert model: the growth and the preferential attachment. [24] By "growth" is meant a growth process where, over an extended period of time, new nodes join an already existing system, a network (like the World Wide Web which has grown by ...
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).
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 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
This model is useful when dealing with data that exhibits exponential growth or decay, while the errors continue to grow as the independent value grows (i.e., heteroscedastic error). As above, in a log-log linear model the relationship between the variables is expressed as a power law.
This model is often referred to as the exponential law. [5] It is widely regarded in the field of population ecology as the first principle of population dynamics, [6] with Malthus as the founder. The exponential law is therefore also sometimes referred to as the Malthusian Law. [7]
Exponential dispersion model; Exponential distribution; Exponential error; Exponential factorial; Exponential family; Exponential field; Exponential formula; Exponential function; Exponential generating function; Exponential-Golomb coding; Exponential growth; Exponential hierarchy; Exponential integral; Exponential integrator; Exponential map ...