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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 ...
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
A chi-squared distribution with 2 degrees of freedom (k = 2) is an exponential distribution with a mean value of 2 (rate λ = 1/2 .) A Weibull distribution with shape parameter k = 1 and rate parameter β is an exponential distribution with rate parameter β.
In studies of the networks of citations between scientific papers, Derek de Solla Price showed in 1965 that the number of links to papers—i.e., the number of citations they receive—had a heavy-tailed distribution following a Pareto distribution or power law, and thus that the citation network is scale-free. He did not however use the term ...
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
Pareto distribution, for a single such quantity whose log is exponentially distributed; the prototypical power law distribution Uniformly distributed quantities [ edit ]
A fat-tailed distribution is a distribution for which the probability density function, for large x, goes to zero as a power . Since such a power is always bounded below by the probability density function of an exponential distribution, fat-tailed distributions are always heavy-tailed.
The multivariate generalized normal distribution, i.e. the product of exponential power distributions with the same and parameters, is the only probability density that can be written in the form () = (‖ ‖) and has independent marginals. [14]