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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 ...
Considerations of the shape of a distribution arise in statistical data analysis, where simple quantitative descriptive statistics and plotting techniques such as histograms can lead on to the selection of a particular family of distributions for modelling purposes. The normal distribution, often called the "bell curve" Exponential distribution
negative skew: The left tail is longer; the mass of the distribution is concentrated on the right of the figure. The distribution is said to be left-skewed , left-tailed , or skewed to the left , despite the fact that the curve itself appears to be skewed or leaning to the right; left instead refers to the left tail being drawn out and, often ...
It is customary to transform data logarithmically to fit symmetrical distributions (like the normal and logistic) to data obeying a distribution that is positively skewed (i.e. skew to the right, with mean > mode, and with a right hand tail that is longer than the left hand tail), see lognormal distribution and the loglogistic distribution. A ...
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 total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot. Histograms are sometimes confused with bar charts. In a histogram, each bin is for a different range of values, so altogether the histogram ...
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The exponentially modified normal distribution is another 3-parameter distribution that is a generalization of the normal distribution to skewed cases. The skew normal still has a normal-like tail in the direction of the skew, with a shorter tail in the other direction; that is, its density is asymptotically proportional to for some positive .