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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 uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
Beta distribution, for a single probability (real number between 0 and 1); conjugate to the Bernoulli distribution and binomial distribution; Gamma distribution, for a non-negative scaling parameter; conjugate to the rate parameter of a Poisson distribution or exponential distribution, the precision (inverse variance) of a normal distribution, etc.
In economics the Pareto index, named after the Italian economist and sociologist Vilfredo Pareto, is a measure of the breadth of income or wealth distribution. It is one of the parameters specifying a Pareto distribution and embodies the Pareto principle. As applied to income, the Pareto principle is sometimes stated in popular expositions by ...
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 terms "distribution" and "family" are often used loosely: Specifically, an exponential family is a set of distributions, where the specific distribution varies with the parameter; [a] however, a parametric family of distributions is often referred to as "a distribution" (like "the normal distribution", meaning "the family of normal distributions"), and the set of all exponential families ...
In multi-objective optimization, the Pareto front (also called Pareto frontier or Pareto curve) is the set of all Pareto efficient solutions. [1] The concept is widely used in engineering . [ 2 ] : 111–148 It allows the designer to restrict attention to the set of efficient choices, and to make tradeoffs within this set, rather than ...
If the Pareto index α, which is one of the parameters characterizing a Pareto distribution, is chosen as α = log 4 5 ≈ 1.16, then one has 80% of effects coming from 20% of causes. [8] The term 80/20 is only a shorthand for the general principle at work. In individual cases, the distribution could be nearer to 90/5 or 70/40.