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The long tail is the name for a long-known feature of some statistical distributions (such as Zipf, power laws, Pareto distributions and general Lévy distributions). In "long-tailed" distributions a high-frequency or high-amplitude population is followed by a low-frequency or low-amplitude population which gradually "tails off" asymptotically ...
To the right is the long tail, and to the left are the few that dominate (also known as the 80–20 rule). In statistics , a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent : one ...
These characteristics can be clearly seen on the graph above to the right. A characteristic of long-tail distributions is that if the logarithm of both the range and the domain is taken, the tail of the long-tail distribution is approximately linear over many orders of magnitude. [9]
The characteristic curved 'long tail' distribution, when plotted on a linear scale, masks the underlying simplicity of the function when plotted on a log-log graph, which then takes the form of a straight line with negative gradient: It follows from the formula for the probability density function that for x ≥ x m,
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.
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.
WASHINGTON/HAVANA (Reuters) -U.S. Secretary of State Marco Rubio said the U.S. would once again restrict financial transactions with many Cuban military- and government-linked entities, just weeks ...
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.