|Posted by [email protected] on July 6, 2014 at 11:30 PM|
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In statistics, 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. A probability distribution is said to have a long tail, if a larger share of population rests within its tail than would under a normal distribution. A long-tail distribution will arise with the inclusion of many values unusually far from the mean, which increase the magnitude of the skewness of the distribution. A long-tailed distribution is a particular type of heavy-tailed distribution.
The term long tail has gained popularity in recent times as describing the retailing strategy of selling a large number of unique items with relatively small quantities sold of each—usually in addition to selling fewer popular items in large quantities. 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 elaborated the concept in his book The Long Tail: Why the Future of Business Is Selling Less of More.
The distribution and inventory costs of businesses successfully applying this strategy allow them to realize significant profit out of selling small volumes of hard-to-find items to many customers instead of only selling large volumes of a reduced number of popular items. The total sales of this large number of "non-hit items" is called "the long tail".
Given enough choice, a large population of customers, and negligible stocking and distribution costs, the selection and buying pattern of the population results in the demand across products having a power law distribution or Pareto distribution. It is important to understand why some distributions are normal vs. long tail (power) distributions. Chris Anderson argues that while quantities such as human height or IQ follow a normal distribution, in scale-free networks with preferential attachments, power law distributions are created, i.e. because some nodes are more connected than others (like Malcolm Gladwell’s “mavens” in The Tipping Point)
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).
A frequency distribution with a long tail has been studied by statisticians since at least 1946. The term has also been used in the financeand 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".
The long tail is the name for a long-known feature of some statistical distributions (such as Zipf, power laws, Pareto distributions and general Lévy distributions). In "long-tailed" distributions a high-frequency or high-amplitude population is followed by a low-frequency or low-amplitude population which gradually "tails off" asymptotically. The events at the far end of the tail have a very low probability of occurrence.
As a rule of thumb, for such population distributions the majority of occurrences (more than half, and where the Pareto principle applies, 80%) are accounted for by the first 20% of items in the distribution. What is unusual about a long-tailed distribution is that the most frequently occurring 20% of items represent less than 50% of occurrences; or in other words, the least frequently occurring 80% of items are more important as a proportion of the total population.
Power law distributions or functions characterize an important number of behaviors from nature and human endeavor. This fact has given rise to a keen scientific and social interest in such distributions, and the relationships that create them. The observation of such a distribution often points to specific kinds of mechanisms, and can often indicate a deep connection with other, seemingly unrelated systems. Examples of behaviors that exhibit long-tailed distribution are the occurrence of certain words in a given language, the income distribution of a business or the intensity of earthquakes (see: Gutenberg–Richter law).
Chris Anderson's and Clay Shirky's articles highlight special cases in which we are able to modify the underlying relationships and evaluate the impact on the frequency of events. In those cases the infrequent, low-amplitude (or low-revenue) events – the long tail, represented here by the portion of the curve to the right of the 20th percentile – can become the largest area under the line. This suggests that a variation of one mechanism (internet access) or relationship (the cost of storage) can significantly shift the frequency of occurrence of certain events in the distribution. The shift has a crucial effect in probability and in the customer demographics of businesses like mass media and online sellers.
However, the long tails characterizing distributions such as the Gutenberg–Richter law or the words-occurrence Zipf's law, and those highlighted by Anderson and Shirky are of very different, if not opposite, nature: Anderson and Shirky refer to frequency-rank relations, whereas the Gutenberg–Richter law and the Zipf's law are probability distributions. Therefore, in these latter cases "tails" correspond to large-intensity events such as large earthquakes and most popular words, who dominate the distributions. By contrast, the long tails in the frequency-rank plots highlighted by Anderson and Shirky would rather correspond to short tails in the associated probability distributions, and therefore illustrate an opposite phenomenon compared to the Gutenberg–Richter and the Zipf's laws.