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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.
negative skew: The left tail is longer; the mass of the distribution is concentrated on the right of the figure. The distribution is said to be left-skewed, left-tailed, or skewed to the left, despite the fact that the curve itself appears to be skewed or leaning to the right; left instead refers to the left tail being drawn out and, often, the ...
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 ...
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 ...
Heavy-tailed distribution; L. Long tail; Long-tail traffic; P. Pareto principle; Pickands–Balkema–De Haan theorem; Z. Zipf's law This page was last edited on 7 ...
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.
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A Lévy flight is a random walk in which the step-lengths have a stable distribution, [1] a probability distribution that is heavy-tailed. When defined as a walk in a space of dimension greater than one, the steps made are in isotropic random directions. Later researchers have extended the use of the term "Lévy flight" to also include cases ...