The Pareto principle states that for many outcomes, roughly 80% of consequences come from 20% of causes (the "vital few"). Other names for this principle are the 80/20 rule, the law of the vital few, or the principle of factor sparsity.
Management consultant Joseph M. Juran developed the concept in the context of quality control and improvement after reading the works of Italian sociologist and economist Vilfredo Pareto, who wrote about the 80/20 connection while teaching at the University of Lausanne. In his first work, Cours d'économie politique, Pareto showed that approximately 80% of the land in the Kingdom of Italy was owned by 20% of the population. The Pareto principle is only tangentially related to the Pareto efficiency.
Mathematically, the 80/20 rule is roughly described by a power law distribution (also known as a Pareto distribution) for a particular set of parameters. Many natural phenomena distribute according to power law statistics. It is an adage of business management that "80% of sales come from 20% of clients."
In 1941, Joseph M. Juran, a Romanian-born American engineer, came across the work of Italian polymath Vilfredo Pareto. Pareto noted that approximately 80% of Italy's land was owned by 20% of the population. Juran applied the observation that 80% of an issue is caused by 20% of the causes to quality issues. Later during his career, Juran preferred to describe this as "the vital few and the useful many" to highlight that the contribution of the remaining 80% should not be discarded entirely.
Pareto's observation was in connection with population and wealth. Pareto noticed that approximately 80% of Italy's land was owned by 20% of the population. He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied (see concentration of land ownership).
A chart that gave the effect a very visible and comprehensible form, the so-called "champagne glass" effect, was contained in the 1992 United Nations Development Program Report, which showed that the distribution of global income is very uneven, with the richest 20% of the world's population receiving 82.
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Zipf's law (zɪf, ts͡ɪpf) is an empirical law that often holds, approximately, when a list of measured values is sorted in decreasing order. It states that the value of the nth entry is inversely proportional to n. The best known instance of Zipf's law applies to the frequency table of words in a text or corpus of natural language: Namely, it is usually found that the most common word occurs approximately twice as often as the next common one, three times as often as the third most common, and so on.
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, 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 that a large portion of wealth is held by a small fraction of the population.
In statistics and business, a long tail of some distributions of numbers is the portion of the distribution having many occurrences far from the "head" or central part of the distribution. The distribution could involve popularities, random numbers of occurrences of events with various probabilities, etc. The term is often used loosely, with no definition or an arbitrary definition, but precise definitions are possible. In statistics, the term long-tailed distribution has a narrow technical meaning, and is a subtype of heavy-tailed distribution.
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AMER INST MATHEMATICAL SCIENCES-AIMS2021
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The purpose of this article is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution, ...
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