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Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.
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
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 .
A significant aspect of the Pareto frontier in economics is that, at a Pareto-efficient allocation, the marginal rate of substitution is the same for all consumers. [5] A formal statement can be derived by considering a system with m consumers and n goods, and a utility function of each consumer as = where = (,, …,) is the vector of goods, both for all i.
In statistics, a multivariate Pareto distribution is a multivariate extension of a univariate Pareto distribution. [1] There are several different types of univariate Pareto distributions including Pareto Types I−IV and Feller−Pareto. [2] Multivariate Pareto distributions have been defined for many of these types.
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 ...
Pareto interpolation is a method of estimating the median and other properties of a population that follows a Pareto distribution. It is used in economics when analysing the distribution of incomes in a population, when one must base estimates on a relatively small random sample taken from the population.
The Mazziotta–Pareto index (MPI) is a composite index [1] (OECD, 2008 [2]) for summarizing a set of individual indicators that are assumed to be not fully substitutable. [3] It is based on a non-linear function which, starting from the arithmetic mean of the normalized indicators, introduces a penalty for the units with unbalanced values of the indicators (De Muro et al., 2011 [4]).