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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.
Tail: [12] the regions ... A discrete probability distribution is the probability distribution of a random ... "Probability distribution", Encyclopedia of Mathematics ...
Heavy-tailed distribution; L. Long tail; Long-tail traffic; P. Pareto principle; Pickands–Balkema–De Haan theorem; Z. Zipf's law
A bimodal distribution would have two high points rather than one. The shape of a distribution is sometimes characterised by the behaviours of the tails (as in a long or short tail). For example, a flat distribution can be said either to have no tails, or to have short tails.
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 ...
This is called the complementary cumulative distribution function (ccdf) or simply the tail distribution or exceedance, and is defined as ¯ = (>) = (). This has applications in statistical hypothesis testing , for example, because the one-sided p-value is the probability of observing a test statistic at least as extreme as the one observed.
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In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.