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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 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.
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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 .
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 ...
Heterodontosauridae is a family of ornithischian dinosaurs that were likely among the most basal (primitive) members of the group. Their phylogenetic placement is uncertain but they are most commonly found to be primitive, outside of the group Genasauria. [2]
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 ...
In probability theory, the tail dependence of a pair of random variables is a measure of their comovements in the tails of the distributions. The concept is used in extreme value theory . Random variables that appear to exhibit no correlation can show tail dependence in extreme deviations.