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.

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.

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 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.

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.

An example of a power law graph showing popularity ranking.

To the right (yellow) is the long tail; to the left (green) are the few that dominate.

In this example, the cutoff is chosen so that areas of both regions are equal.

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.

crowdsourcing, crowdcasting, peer-to-peer), economic models, and marketing (viral marketing).

The distribution and inventory costs of businesses successfully applying a long tail 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. 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).