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In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions.It is often used to model the tails of another distribution. It is specified by three parameters: location , scale , and shape
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, [2] is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend ...
The generalized Pareto distribution has a support which is either bounded below only, or bounded both above and below The metalog distribution , which provides flexibility for unbounded, bounded, and semi-bounded support, is highly shape-flexible, has simple closed forms, and can be fit to data using linear least squares.
The class of underlying distribution functions are related to the class of the distribution functions satisfying the Fisher–Tippett–Gnedenko theorem. [ 3 ] Since a special case of the generalized Pareto distribution is a power-law, the Pickands–Balkema–De Haan theorem is sometimes used to justify the use of a power-law for modeling ...
A common assumption for the first is the Poisson distribution, with the generalized Pareto distribution being used for the exceedances. A tail-fitting can be based on the Pickands–Balkema–de Haan theorem. [5] [6]
In probability and statistics, the generalized beta distribution [1] ... (also referred to as the double Pareto distribution [9]) is defined by: [10]
In probability theory and statistics, the Zipf–Mandelbrot law is a discrete probability distribution.Also known as the Pareto–Zipf law, it is a power-law distribution on ranked data, named after the linguist George Kingsley Zipf, who suggested a simpler distribution called Zipf's law, and the mathematician Benoit Mandelbrot, who subsequently generalized it.
The q-exponential is a special case of the generalized Pareto distribution where =, =, = (). The q-exponential is the generalization of the Lomax distribution (Pareto Type II), as it extends this distribution to the cases of finite support.