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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. 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.

  4. Tail dependence - Wikipedia

    en.wikipedia.org/wiki/Tail_dependence

    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.

  5. 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, 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.

  6. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    In these cases, the probability distribution is supported on the image of such curve, and is likely to be determined empirically, rather than finding a closed formula for it. [25] One example is shown in the figure to the right, which displays the evolution of a system of differential equations (commonly known as the Rabinovich–Fabrikant ...

  7. Power law - Wikipedia

    en.wikipedia.org/wiki/Power_law

    Usually, this estimator is the proportion of times that the number occurs in the data set. If the points in the plot tend to converge to a straight line for large numbers in the x axis, then the researcher concludes that the distribution has a power-law tail. Examples of the application of these types of plot have been published. [61]

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    mail.aol.com

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  9. Long tail - Wikipedia

    en.wikipedia.org/wiki/Long_tail

    The long tail is a potential market and, as the examples illustrate, the distribution and sales channel opportunities created by the Internet often enable businesses to tap that market successfully. In his Wired article Anderson opens with an anecdote about creating a niche market for books on Amazon.