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The distribution of a random variable X with distribution function F is said to have a long right tail [1] if for all t > 0, [> + >] =,or equivalently ¯ (+) ¯ (). This has the intuitive interpretation for a right-tailed long-tailed distributed quantity that if the long-tailed quantity exceeds some high level, the probability approaches 1 that it will exceed any other higher level.
In statistics, the term long-tailed distribution has a narrow technical meaning, and is a subtype of heavy-tailed distribution. [2] [3] [4] Intuitively, a distribution is (right) long-tailed if, for any fixed amount, when a quantity exceeds a high level, it almost certainly exceeds it by at least that amount: large quantities are probably even ...
Research in this area started to gain momentum in 2005 after the publication of A.-L. Barabási's seminal paper The origin of bursts and heavy tails in human dynamics. [1] that introduced a queuing model that was alleged to be capable of explaining the long tailed distribution of inter event times that naturally occur in human activity.
A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. [ when defined as? ] In common usage, the terms fat-tailed and heavy-tailed are sometimes synonymous; fat-tailed is sometimes also defined as a subset of heavy-tailed.
Heavy-tail distributions have properties that are qualitatively different from commonly used (memoryless) distributions such as the exponential distribution. The Hurst parameter H is a measure of the level of self-similarity of a time series that exhibits long-range dependence, to which the heavy-tail distribution can be applied.
Mathematically, a strict power law cannot be a probability distribution, but a distribution that is a truncated power function is possible: () = for > where the exponent (Greek letter alpha, not to be confused with scaling factor used above) is greater than 1 (otherwise the tail has infinite area), the minimum value is needed otherwise the ...
The tail is also more exposed and active than the backbone, so there's a greater chance of injury. Number 1: The term 'hair of the dog' comes from the tail. Back in the day, Pliny the Elder said ...
Head/tail breaks is a clustering algorithm for data with a heavy-tailed distribution such as power laws and lognormal distributions. The heavy-tailed distribution can be simply referred to the scaling pattern of far more small things than large ones, or alternatively numerous smallest, a very few largest, and some in between the smallest and ...