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Power Laws
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent: one quantity varies as a power of another. The change is independent of the initial size of those quantities. For instance, the area of a square has a power law relationship with the length of its side, since if the length is doubled, the area is multiplied by 2, while if the length is tripled, the area is multiplied by 3, and so on. Empirical examples The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, cloud sizes, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words in most languages, frequencies of family names, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Long Tail
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. Intuitively, a distribution is (right) long-tailed if, for any fixed amount, when a quantity exceeds a high level, it almost certainly exceeds it by at least that amount: large quantities are probably even larger. Note that there is no sense of ''the'' "long tail" of a distribution, but only the ''property'' of a distribution being long-tailed. In business, the term ''long tail'' is applied to rank-size distributions or rank-fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
