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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.
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 ...
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 ...
A subexponential distribution may be: A kind of heavy-tailed distribution . A distribution with sufficiently light tails so that a certain Orlicz norm of the distribution is finite, or equivalently has distribution function dominated by that of an exponential random variable .
Also, researchers usually have to face the problem of deciding whether or not a real-world probability distribution follows a power law. As a solution to this problem, Diaz [57] proposed a graphical methodology based on random samples that allow visually discerning between different types of tail behavior. This methodology uses bundles of ...
Heavy-tailed refers to a probability distribution, and long-range dependent refers to a property of a time series and so these should be used with care and a distinction should be made. The terms are distinct although superpositions of samples from heavy-tailed distributions aggregate to form long-range dependent time series.
Long-range dependence is closely connected to the theory of heavy-tailed distributions. [7] A distribution is said to have a heavy tail if [>] = > One example of a heavy-tailed distribution is the Pareto distribution. Examples of processes that can be described using heavy-tailed distributions include traffic processes, such as packet inter ...