Search results
Results from the WOW.Com Content Network
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 ...
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 ...
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 normal distribution is usually regarded as having short tails, while an exponential distribution has exponential tails and a Pareto ...
Main page; Contents; Current events; Random article; About Wikipedia; Contact us
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 distribution of has no closed-form expression, but can be reasonably approximated by another log-normal distribution at the right tail. [36] Its probability density function at the neighborhood of 0 has been characterized [ 35 ] and it does not resemble any log-normal distribution.
A long-tailed or heavy-tailed distribution is one that assigns relatively high probabilities to regions far from the mean or median. A more formal mathematical definition is given below. In the context of teletraffic engineering a number of quantities of interest have been shown to have a long-tailed distribution. For example, if we consider ...
Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of classical financial models. These classical models of financial time series typically assume homoskedasticity and normality and as such cannot explain stylized phenomena such as skewness, heavy tails, and volatility clustering of the empirical asset returns in ...