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In statistics and business, a long tail of some distributions of numbers is the portion of the distribution having a large number of 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 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; see that article for details.〔Levine, David M.; Stephan, David; Krehbiel, Timothy C.; Berenson, Mark L. ''Statistics for Managers using Microsoft Excel''. 3rd edition. Prentice Hall, 2002, p. 124.〕 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: big quantities are probably even bigger. Note that statistically, 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-frequency distributions (primarily of popularity), which often form power laws and are thus long-tailed distributions in the statistical sense. This is used to describe the retailing strategy of selling a large number of unique items with relatively small quantities sold of each (the "long tail") — usually in addition to selling fewer popular items in large quantities (the "head"). Sometimes an intermediate category is also included, variously called the ''body'', ''belly'', ''torso'', or ''middle''. The specific cutoff of what part of a distribution is ''the'' "long tail" is often arbitrary, but in some cases may be specified objectively; see segmentation of rank-size distributions. The long tail concept has found some ground for application, research, and experimentation. It is a term used in online business, mass media, micro-finance (Grameen Bank, for example), user-driven innovation (Eric von Hippel), and social network mechanisms (e.g. crowdsourcing, crowdcasting, peer-to-peer), economic models, and marketing (viral marketing). ==History== A frequency distribution with a long tail has been studied by statisticians since at least 1946.〔A search for the phrase "long tail" in the database MathSciNet yielded 81 hits, the earliest being a 1946 paper by Brown and Tukey in the Annals of Mathematical Statistics (volume 17, pages 1–12).〕 The term has also been used in the finance〔Bessis, Jöel "Risk Management in Banking". Wiley, 1995〕 and insurance business〔 for many years. The work of Benoît Mandelbrot in the 1950s and later has led to him being referred to as "the father of long tails".〔Obrist, Hans Ulrich ("The Father of Long Tales. An interview with Benoît Mandelbrot" ), Edge.org, 2008〕 The long tail was popularized by Chris Anderson in an October 2004 ''Wired'' magazine article, in which he mentioned Amazon.com, Apple and Yahoo! as examples of businesses applying this strategy.〔Anderson, Chris. ("The Long Tail" ) ''Wired'', October 2004.〕 Anderson elaborated the concept in his book ''The Long Tail: Why the Future of Business Is Selling Less of More''.〔(【引用サイトリンク】url=http://www.econtalk.org/archives/2006/08/chris_anderson.html )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「long tail」の詳細全文を読む スポンサード リンク
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