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  2. Heavy-tailed distribution - Wikipedia

    en.wikipedia.org/wiki/Heavy-tailed_distribution

    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.

  3. Fat-tailed distribution - Wikipedia

    en.wikipedia.org/wiki/Fat-tailed_distribution

    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 ...

  4. Category:Tails of probability distributions - Wikipedia

    en.wikipedia.org/wiki/Category:Tails_of...

    Pages in category "Tails of probability distributions" The following 10 pages are in this category, out of 10 total. This list may not reflect recent changes .

  5. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random ...

  6. Long tail - Wikipedia

    en.wikipedia.org/wiki/Long_tail

    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 ...

  7. Cumulative distribution function - Wikipedia

    en.wikipedia.org/wiki/Cumulative_distribution...

    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.

  8. Shape of a probability distribution - Wikipedia

    en.wikipedia.org/wiki/Shape_of_a_probability...

    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.

  9. Q-function - Wikipedia

    en.wikipedia.org/wiki/Q-function

    In statistics, the Q-function is the tail distribution function of the standard normal distribution. [1] [2] In other words, () is the probability that a normal (Gaussian) random variable will obtain a value larger than standard deviations.