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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
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 long tail has possible implications for culture and politics. Where the opportunity cost of inventory storage and distribution is high, only the most popular products are sold. But where the long tail works, minority tastes become available and individuals are presented with a wider array of choices.
In the study, genetically engineered mice exhibit varying tail lengths: from no tail to long tails. (Arrowheads highlight differences in tail phenotypes. "cv" is "caudal vertebrae"; "sv" is ...
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 ...
The most extreme case of a fat tail is given by a distribution whose tail decays like a power law. A variety of Cauchy distributions for various location and scale parameters. Cauchy distributions are examples of fat-tailed distributions. That is, if the complementary cumulative distribution of a random variable X can be expressed as [citation ...
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