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127-397: 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

254-526: A "strikingly different way of looking at the world". The term " tipping point " comes from the moment in an epidemic when the virus reaches critical mass and begins to spread at a much higher rate. Gladwell's theories of crime were heavily influenced by the " broken windows theory " of policing, and Gladwell is credited for packaging and popularizing the theory in a way that was implementable in New York City. Gladwell's theoretical implementation bears

381-658: A 5:15 mile. He had his first child, a daughter, in 2022. In 2005, Time named Gladwell one of its 100 most influential people. In 2007, he received the American Sociological Association 's first Award for Excellence in the Reporting of Social Issues. The same year, he received an honorary degree from the University of Waterloo. In 2011, he was named a Member of the Order of Canada ,

508-581: A Dutch genius and his homemade computer, a band of brothers in central Alabama, a British psychopath, and pyromaniacal chemists at Harvard to examine one of the greatest moral challenges in modern American history. Gladwell's eighth book, Revenge of the Tipping Point was released in October 2024. The book is a sequel to his best seller The Tipping Point, which was released in 2000. The book discusses social epidemics and tipping points, this time with

635-576: A SOC ( Information security operations center ). Frequency distributions with long tails have been studied by statisticians since at least 1946. The term has also been used in the finance 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". 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

762-690: A bachelor's degree in history from Trinity College of the University of Toronto , in 1984. Gladwell decided to pursue advertising as a career after college. After being rejected by every advertising agency he applied to, he accepted a journalism position at conservative magazine The American Spectator and moved to Indiana . He subsequently wrote for Insight on the News , a conservative magazine owned by Sun Myung Moon 's Unification Church . In 1987, Gladwell began covering business and science for The Washington Post , where he worked until 1996. In

889-410: A bias toward popular products, creating positive feedback , and actually reduce the long tail. A Wharton study details this phenomenon along with several ideas that may promote the long tail and greater diversity. A 2010 study conducted by Wenqi Zhou and Wenjing Duan further points out that the demand side factor (online user reviews) and the supply side factor (product variety) interplay to influence

1016-429: A common distribution function F {\displaystyle F} , the convolution of F {\displaystyle F} with itself, written F ∗ 2 {\displaystyle F^{*2}} and called the convolution square, is defined using Lebesgue–Stieltjes integration by: and the n -fold convolution F ∗ n {\displaystyle F^{*n}}

1143-425: A computed residual or filtered data from a large class of models and estimators, including mis-specified models and models with errors that are dependent. Note that both Pickand's and Hill's tail-index estimators commonly make use of logarithm of the order statistics. The ratio estimator (RE-estimator) of the tail-index was introduced by Goldie and Smith. It is constructed similarly to Hill's estimator but uses

1270-425: 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

1397-569: 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 many 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

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1524-512: A doubling of this influence leads to a 50% increase in revenues from the least popular one-fifth of books. The long-tail distribution applies at a given point in time, but over time the relative popularity of the sales of the individual products will change. Although the distribution of sales may appear to be similar over time, the positions of the individual items within it will vary. For example, new items constantly enter most fashion markets. A recent fashion-based model of consumer choice , which

1651-474: A handful of links going into them. Anderson described the effects of the long tail on current and future business models beginning with a series of speeches in early 2004 and with the publication of a Wired magazine article in October 2004. Anderson later extended it into the book The Long Tail: Why the Future of Business is Selling Less of More (2006). Anderson argues that products in low demand or that have

1778-455: 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

1905-401: A large group of users that are in the low-intensity area of the distribution. It is their collaboration and aggregated work that results in an innovation effort. Social innovation communities formed by groups of users can perform rapidly the trial and error process of innovation, share information, test and diffuse the results. Eric von Hippel of MIT's Sloan School of Management defined

2032-410: 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

2159-466: A long tail is the cost of inventory storage and distribution. Where inventory storage and distribution costs are insignificant, it becomes economically viable to sell relatively unpopular products; however, when storage and distribution costs are high, only the most popular products can be sold. For example, a traditional movie rental store has limited shelf space, which it pays for in the form of building overhead ; to maximize its profits, it must stock only

2286-441: A low sales volume can collectively make up a market share that rivals or exceeds the relatively few current bestsellers and blockbusters, if the store or distribution channel is large enough. Anderson cites earlier research by Erik Brynjolfsson , Yu (Jeffrey) Hu , and Michael D. Smith , that showed that a significant portion of Amazon.com's sales come from obscure books that are not available in brick-and-mortar stores. The long tail

2413-523: A non-random "tuning parameter". A comparison of Hill-type and RE-type estimators can be found in Novak. Nonparametric approaches to estimate heavy- and superheavy-tailed probability density functions were given in Markovich. These are approaches based on variable bandwidth and long-tailed kernel estimators; on the preliminary data transform to a new random variable at finite or infinite intervals, which

2540-510: 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 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

2667-503: A particular incident, he was apprehended by three police officers while walking in downtown Manhattan because his curly hair matched the profile of a rapist, despite the fact the suspect looked nothing like him otherwise. Gladwell's The Tipping Point (2000) and Blink (2005) were international bestsellers. The Tipping Point sold more than two million copies in the United States. Blink sold equally well. As of November 2008,

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2794-542: A personal elucidation of the 10,000-hour rule he popularized in Outliers , Gladwell notes, "I was a basket case at the beginning, and I felt like an expert at the end. It took 10 years—exactly that long." When Gladwell started at The New Yorker in 1996, he wanted to "mine current academic research for insights, theories, direction, or inspiration". His first assignment was to write a piece about fashion. Instead of writing about high-class fashion, Gladwell opted to write

2921-456: A piece about a man who manufactured T-shirts, saying: "[I]t was much more interesting to write a piece about someone who made a T-shirt for $ 8 than it was to write about a dress that costs $ 100,000. I mean, you or I could make a dress for $ 100,000, but to make a T-shirt for $ 8—that's much tougher." Gladwell gained popularity with two New Yorker articles, both written in 1996: "The Tipping Point" and "The Coolhunt". These two pieces would become

3048-420: A popular genre supporting the long tail theory. An Amazon employee described the long tail as follows: "We sold more books today that didn't sell at all yesterday than we sold today of all the books that did sell yesterday." Anderson has explained the term as a reference to the tail of a demand curve . The term has since been re derived from an XY graph that is created when charting popularity to inventory. In

3175-454: A power (meaning they are not fat-tailed). An example is the log-normal distribution . Many other heavy-tailed distributions such as the log-logistic and Pareto distribution are, however, also fat-tailed. There are parametric and non-parametric approaches to the problem of the tail-index estimation. To estimate the tail-index using the parametric approach, some authors employ GEV distribution or Pareto distribution ; they may apply

3302-515: A sequence of independent and identically distributed random variables with distribution function F ∈ D ( H ( ξ ) ) {\displaystyle F\in D(H(\xi ))} , the maximum domain of attraction of the generalized extreme value distribution H {\displaystyle H} , where ξ ∈ R {\displaystyle \xi \in \mathbb {R} } . The sample path

3429-431: A series of long-tail marketing techniques, most of them based on extensive use of internet technologies. Among the most representative are: The long tail has possible implications for culture and politics . Where the opportunity cost of inventory storage and distribution is high, only the most popular products are sold. But where the long tail works, minority tastes become available and individuals are presented with

3556-460: A striking resemblance to the " stop-and-frisk " policies of the NYPD. However, in the decade and a half since its publication, The Tipping Point and Gladwell have both come under fire for the tenuous link between "broken windows" and New York City's drop in violent crime. During a 2013 interview with BBC journalist Jon Ronson for The Culture Show , Gladwell admitted that he was "too in love with

3683-522: A talk about innovation for a group of entrepreneurs in Los Angeles a while back, sponsored by Bank of America. They liked the talk, and asked me to give the same talk at two more small business events—in Dallas and yesterday in D.C. That's the extent of it. No different from any other speaking gig. I haven't been asked to do anything else and imagine that's it. In 2012, CBS 's 60 Minutes attributed

3810-479: A three-city speaking tour put on by Bank of America . The program was titled "Bank of America Small Business Speaker Series: A Conversation with Malcolm Gladwell". Paul Starobin, writing in the Columbia Journalism Review , said the engagement's "entire point seemed to be to forge a public link between a tarnished brand (the bank), and a winning one (a journalist often described in profiles as

3937-435: A time in which game-based training devices or simulations will be available for thousands of different job descriptions. The banking business has used internet technology to reach an increasing number of customers. The most important shift in business model due to the long tail has come from the various forms of microfinance developed. As opposed to e-tailers, micro-finance is a distinctly low technology business. Its aim

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4064-701: A total of 49 episodes. Gladwell is a Christian. His family attended Above Bar Church in Southampton, U.K., and later Gale Presbyterian in Elmira when they moved to Canada. His parents and siblings are part of the Mennonite community in Southwestern Ontario. Gladwell wandered away from his Christian roots when he moved to New York, only to rediscover his faith during the writing of David and Goliath and his encounter with Wilma Derksen regarding

4191-424: A unique opportunity for companies to leverage interactive and internet-based technologies to give their users a voice and enable them to participate in the innovation process. By doing so, companies can gain valuable insights into their customer's needs and preferences, which can help drive product development and innovation. By creating a platform for their users to share their ideas and feedback, companies can harness

4318-400: A voice and to enable them to do innovation work that is useful to the company. Given the diminishing cost of communication and information sharing (by analogy to the low cost of storage and distribution, in the case of e-tailers ), long-tailed user driven innovation will gain importance for businesses. In following a long-tailed innovation strategy, the company is using the model to tap into

4445-416: A wider array of choices. The long tail presents opportunities for various suppliers to introduce products in the niche category. These encourage the diversification of products. These niche products open opportunities for suppliers while concomitantly satisfying the demands of many individuals – therefore lengthening the tail portion of the long tail. In situations where popularity is currently determined by

4572-590: A writer. Gladwell's father noted that Malcolm was an unusually single-minded and ambitious boy. When Malcolm was 11, his father, a professor of mathematics and engineering at the University of Waterloo , allowed his son to wander around the offices at his university, which stoked the boy's interest in reading and libraries. In the spring of 1982, Gladwell interned with the National Journalism Center in Washington, D.C. He graduated with

4699-705: Is X t : 1 ≤ t ≤ n {\displaystyle {X_{t}:1\leq t\leq n}} where n {\displaystyle n} is the sample size. If { k ( n ) } {\displaystyle \{k(n)\}} is an intermediate order sequence, i.e. k ( n ) ∈ { 1 , … , n − 1 } , {\displaystyle k(n)\in \{1,\ldots ,n-1\},} , k ( n ) → ∞ {\displaystyle k(n)\to \infty } and k ( n ) / n → 0 {\displaystyle k(n)/n\to 0} , then

4826-412: Is YouTube , where thousands of diverse videos – whose content, production value or lack of popularity make them inappropriate for traditional television – are easily accessible to a wide range of viewers. Heavy-tailed distribution In probability theory , heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than

4953-527: Is a Jamaican psychotherapist . His father, Graham Gladwell, was a mathematics professor from Kent , England. When he was six his family moved from Southampton to the Mennonite community of Elmira, Ontario , Canada. He has two brothers. Throughout his childhood, Malcolm lived in rural Ontario Mennonite country, where he attended a Mennonite church. Research done by historian Henry Louis Gates Jr. revealed that one of Gladwell's maternal ancestors

5080-484: Is a distribution for which the probability density function, for large x, goes to zero as a power x − a {\displaystyle x^{-a}} . Since such a power is always bounded below by the probability density function of an exponential distribution, fat-tailed distributions are always heavy-tailed. Some distributions, however, have a tail which goes to zero slower than an exponential function (meaning they are heavy-tailed), but faster than

5207-512: Is a potential market and, as the examples illustrate, the distribution and sales channel opportunities created by the Internet often enable businesses to tap that market successfully. In his Wired article Anderson opens with an anecdote about creating a niche market for books on Amazon. He writes about a book titled Touching the Void about a near-death mountain climbing accident that took place in

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5334-695: 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 ), knowledge management, and social network mechanisms (e.g. crowdsourcing , crowdcasting , peer-to-peer ), economic models, marketing ( viral marketing ), and IT Security threat hunting within

5461-577: Is also the host of the podcast Revisionist History and co-founder of the podcast company Pushkin Industries . Gladwell's writings often deal with the unexpected implications of research in the social sciences, such as sociology and psychology , and make frequent and extended use of academic work. Gladwell was appointed to the Order of Canada in 2011. Gladwell was born in Fareham , Hampshire , England . His mother Joyce (née Nation) Gladwell,

5588-497: Is apt to offer generalizations that are banal, obtuse or flat wrong." A writer in The Independent accused Gladwell of posing "obvious" insights. The Register has accused Gladwell of making arguments by weak analogy and commented Gladwell has an "aversion for fact", adding: "Gladwell has made a career out of handing simple, vacuous truths to people and dressing them up with flowery language and an impressionistic take on

5715-549: Is as close to a singular talent as exists today" and Outliers "leaves you mulling over its inventive theories for days afterward". Ian Sample wrote in The Guardian : "Brought together, the pieces form a dazzling record of Gladwell's art. There is depth to his research and clarity in his arguments, but it is the breadth of subjects he applies himself to that is truly impressive." Gladwell's critics have described him as prone to oversimplification. The New Republic called

5842-412: Is asymptotically normal provided k ( n ) → ∞ {\displaystyle k(n)\to \infty } is restricted based on a higher order regular variation property . Consistency and asymptotic normality extend to a large class of dependent and heterogeneous sequences, irrespective of whether X t {\displaystyle X_{t}} is observed, or

5969-466: Is capable of generating power law distributions of sales similar to those observed in practice, takes into account turnover in the relative sales of a given set of items, as well as innovation, in the sense that entirely new items become offered for sale. There may be an optimal inventory size, given the balance between sales and the cost of keeping up with the turnover. An analysis based on this pure fashion model indicates that, even for digital retailers,

6096-611: Is cases where they overlap". The initial inspiration for his first book, The Tipping Point , which was published in 2000, came from the sudden drop of crime in New York City . He wanted the book to have a broader appeal than just crime, however, and sought to explain similar phenomena through the lens of epidemiology . While Gladwell was a reporter for The Washington Post , he covered the AIDS epidemic. He began to take note of "how strange epidemics were", saying epidemiologists have

6223-402: Is defined inductively by the rule: The tail distribution function F ¯ {\displaystyle {\overline {F}}} is defined as F ¯ ( x ) = 1 − F ( x ) {\displaystyle {\overline {F}}(x)=1-F(x)} . A distribution F {\displaystyle F} on the positive half-line

6350-400: Is more convenient for the estimation and then inverse transform of the obtained density estimate; and "piecing-together approach" which provides a certain parametric model for the tail of the density and a non-parametric model to approximate the mode of the density. Nonparametric estimators require an appropriate selection of tuning (smoothing) parameters like a bandwidth of kernel estimators and

6477-417: Is often known as the principle of the single big jump or catastrophe principle. A distribution F {\displaystyle F} on the whole real line is subexponential if the distribution F I ( [ 0 , ∞ ) ) {\displaystyle FI([0,\infty ))} is. Here I ( [ 0 , ∞ ) ) {\displaystyle I([0,\infty ))}

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6604-401: Is said to have a heavy (right) tail if the moment generating function of X , M X ( t ), is infinite for all t  > 0. That means This is also written in terms of the tail distribution function as The distribution of a random variable X with distribution function F is said to have a long right tail if for all t  > 0, or equivalently This has

6731-466: Is subexponential if This implies that, for any n ≥ 1 {\displaystyle n\geq 1} , The probabilistic interpretation of this is that, for a sum of n {\displaystyle n} independent random variables X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}} with common distribution F {\displaystyle F} , This

6858-642: Is the indicator function of the positive half-line. Alternatively, a random variable X {\displaystyle X} supported on the real line is subexponential if and only if X + = max ( 0 , X ) {\displaystyle X^{+}=\max(0,X)} is subexponential. All subexponential distributions are long-tailed, but examples can be constructed of long-tailed distributions that are not subexponential. All commonly used heavy-tailed distributions are subexponential. Those that are one-tailed include: Those that are two-tailed include: A fat-tailed distribution

6985-437: Is the most general in use, and includes all distributions encompassed by the alternative definitions, as well as those distributions such as log-normal that possess all their power moments, yet which are generally considered to be heavy-tailed. (Occasionally, heavy-tailed is used for any distribution that has heavier tails than the normal distribution.) The distribution of a random variable X with distribution function F

7112-567: Is the only guest to have been featured as a headliner at every OZY Fest festival —an annual music and ideas festival produced by OZY Media —other than OZY co-founder and CEO Carlos Watson . Gladwell has also appeared on several television shows for OZY Media, including the Carlos Watson Show (YouTube) and Third Rail With OZY (PBS). Gladwell has a chapter giving advice in Tim Ferriss 's book Tools of Titans . Gladwell

7239-509: Is to offer very small credits to lower-middle to lower class and poor people, that would otherwise be ignored by the traditional banking business. The banks that have followed this strategy of selling services to the low-frequency long tail of the sector have found out that it can be an important niche, long ignored by consumer banks. The recipients of small credits tend to be very good payers of loans, despite their non-existent credit history. They are also willing to pay higher interest rates than

7366-510: The San Francisco Chronicle 's list of the 50 best non-fiction books of 2008. Fortune described The Tipping Point as "a fascinating book that makes you see the world in a different way". The Daily Telegraph called it "a wonderfully offbeat study of that little-understood phenomenon, the social epidemic". Reviewing Blink , The Baltimore Sun dubbed Gladwell "the most original American journalist since

7493-468: The Getty kouros and psychologist John Gottman 's research on the likelihood of divorce in married couples . Gladwell's hair was the inspiration for Blink . He stated that once he allowed his hair to get longer, he started to get speeding tickets all the time, an oddity considering that he had never gotten one before and that he started getting pulled out of airport security lines for special attention. In

7620-640: The Pickands tail-index estimation is where X ( n − k ( n ) + 1 , n ) = max ( X n − k ( n ) + 1 , … , X n ) {\displaystyle X_{(n-k(n)+1,n)}=\max \left(X_{n-k(n)+1},\ldots ,X_{n}\right)} . This estimator converges in probability to ξ {\displaystyle \xi } . Let ( X t , t ≥ 1 ) {\displaystyle (X_{t},t\geq 1)} be

7747-434: The exponential distribution . In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy. There are three important subclasses of heavy-tailed distributions: the fat-tailed distributions , the long-tailed distributions , and the subexponential distributions . In practice, all commonly used heavy-tailed distributions belong to

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7874-410: The user-driven innovation model, companies can rely on users of their products and services to do a significant part of the innovation work. Users want products that are customized to their needs. They are willing to tell the manufacturer what they really want and how it should work. Companies can make use of a series of tools, such as interactive and internet based technologies, to give their users

8001-555: The "local Markets" such as physical retailers like Target or even Walmart . With the digital and hybrid retailers there is no longer a perimeter on market demands. The adoption of video games and massively multiplayer online games such as Second Life as tools for education and training is starting to show a long-tailed pattern. It costs significantly less to modify a game than it has been to create unique training applications, such as those for training in business, commercial flight, and military missions. This has led some to envision

8128-464: The Gladwellian genre. Gladwell has provided blurbs for "scores of book covers", leading The New York Times to ask, "Is it possible that Mr. Gladwell has been spreading the love a bit too thinly?" Gladwell, who said he did not know how many blurbs he had written, acknowledged, "The more blurbs you give, the lower the value of the blurb. It's the tragedy of the commons ." Gladwell is host of

8255-560: The Gutenberg–Richter and the Zipf's laws. Use of the phrase the long tail in business as "the notion of looking at the tail itself as a new market" of consumers was first coined by Chris Anderson . The concept drew in part from a February 2003 essay by Clay Shirky , "Power Laws, Weblogs and Inequality", which noted that a relative handful of weblogs have many links going into them but "the long tail" of millions of weblogs may have only

8382-472: 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, which 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

8509-479: The Hill tail-index estimator is where X ( i , n ) {\displaystyle X_{(i,n)}} is the i {\displaystyle i} -th order statistic of X 1 , … , X n {\displaystyle X_{1},\dots ,X_{n}} . This estimator converges in probability to ξ {\displaystyle \xi } , and

8636-522: The Peruvian Andes. Anderson states the book got good reviews, but didn't have much commercial success. However, ten years later a book titled Into Thin Air by Jon Krakauer was published and Touching the Void began to sell again. Anderson realized that this was due to Amazon's recommendations. This created a niche market for those who enjoy books about mountain climbing even though it is not considered

8763-594: The advantageous use of the long tail: for example, Netflix finds that in aggregate, "unpopular" movies are rented more than popular movies. An MIT Sloan Management Review article titled "From Niches to Riches: Anatomy of the Long Tail" examined the long tail from both the supply side and the demand side and identifies several key drivers. On the supply side, the authors point out how e-tailers ' expanded, centralized warehousing allows for more offerings, thus making it possible for them to cater to more varied tastes. On

8890-439: The aim of explaining the dark side of contagious phenomena, and offers an alternate history of two of the biggest epidemics of our day: COVID and the opioid crisis. The Tipping Point was named as one of the best books of the decade by The A.V. Club , The Guardian , and The Times . It was also Barnes & Noble 's fifth-best-selling non-fiction book of the decade. Blink was named to Fast Company 's list of

9017-658: The basis for Gladwell's first book, The Tipping Point , for which he received a $ 1 million advance. He continues to write for The New Yorker . Gladwell also served as a contributing editor for Grantland , a sports journalism website founded by former ESPN columnist Bill Simmons . In a July 2002 article in The New Yorker , Gladwell introduced the concept of the "talent myth" that companies and organizations, in his view, incorrectly follow. This work examines different managerial and administrative techniques that companies, both winners and losers, have used. He states that

9144-545: The basis for a model for optimizing the number of each individual item ordered, given its current sales rank and the total number of different titles stocked. From a given country's viewpoint, diplomatic interactions with other countries likewise exhibit a long tail. Strategic partners receive the largest amount of diplomatic attention, while a long tail of remote states obtains just an occasional signal of peace. The fact that even allegedly "irrelevant" countries obtain at least rare amicable interactions by virtually all other states

9271-408: The best business books of 2005. It was also number 5 on Amazon customers' favourite books of 2005, named to The Christian Science Monitor 's best non-fiction books of 2005, and in the top 50 of Amazon customers' favourite books of the decade. Outliers was a number 1 New York Times bestseller for 11 straight weeks and was Time 's number 10 non-fiction book of 2008 as well as named to

9398-448: The bin width of the histogram. The well known data-driven methods of such selection are a cross-validation and its modifications, methods based on the minimization of the mean squared error (MSE) and its asymptotic and their upper bounds. A discrepancy method which uses well-known nonparametric statistics like Kolmogorov-Smirnov's, von Mises and Anderson-Darling's ones as a metric in the space of distribution functions (dfs) and quantiles of

9525-404: The broken-windows notion". He went on to say that he was "so enamored by the metaphorical simplicity of that idea that I overstated its importance". After The Tipping Point, Gladwell published Blink in 2005. The book explains how the human unconscious interprets events or cues as well as how past experiences can lead people to make informed decisions very rapidly. Gladwell uses examples like

9652-475: The collective share of hard-to-find products, thereby creating a longer tail in the distribution of sales. They used a theoretical model to show how a reduction in search costs will affect the concentration in product sales. By analyzing data collected from a multi-channel retailing company, they showed empirical evidence that the Internet channel exhibits a significantly less concentrated sales distribution, when compared with traditional channels. An 80/20 rule fits

9779-472: The concept in his book The Long Tail: Why the Future of Business Is Selling Less of More . Anderson cites research published in 2003 by Erik Brynjolfsson , Yu (Jeffrey) Hu , and Michael D. Smith , who first used a log-linear curve on an XY graph to describe the relationship between Amazon.com sales and sales ranking. They showed that the primary value of the internet to consumers comes from releasing new sources of value by providing access to products in

9906-475: The death of her child. Gladwell was a national class runner and an Ontario High School ( Ontario Federation of School Athletic Associations – OFSAA) champion. He was among Canada's fastest teenagers at 1500 metres , running 4:14 at the age of 13 and 4:05 when aged 14. At university, Gladwell ran 1500 metres in 3:55. In 2014, at the age of 51, he ran a 4:54 at the Fifth Avenue Mile . At 57 he ran

10033-551: The decrease for the hits is more pronounced, indicating the demand shifting from the hits to the niches over time. In addition, they also observe a superstar effect in the presence of the long tail. A small number of very popular products still dominates the demand. In a 2006 working paper titled "Goodbye Pareto Principle, Hello Long Tail", Erik Brynjolfsson , Yu (Jeffrey) Hu , and Duncan Simester found that, by greatly lowering search costs, information technology in general and Internet markets in particular could substantially increase

10160-473: The demand side, tools such as search engines, recommendation software, and sampling tools are allowing customers to find products outside their geographic area. The authors also look toward the future to discuss second-order, amplified effects of Long Tail, including the growth of markets serving smaller niches. Not all recommender systems are equal, however, when it comes to expanding the long tail. Some recommenders (i.e. certain collaborative filters) can exhibit

10287-402: The distribution of product sales in the catalog channel quite well, but in the Internet channel, this rule needs to be modified to a 72/28 rule in order to fit the distribution of product sales in that channel. The difference in the sales distribution is highly significant, even after controlling for consumer differences. The key supply-side factor that determines whether a sales distribution has

10414-493: 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

10541-438: The effect of reducing demand for the most popular products. For example, a small website that focuses on niches of content can be threatened by a larger website which has a variety of information (such as Yahoo) Web content . The big website covers more variety while the small website has only a few niches to choose from. The competitive threat from these niche sites is reduced by the cost of establishing and maintaining them and

10668-427: The effort required for readers to track multiple small web sites. These factors have been transformed by easy and cheap web site software and the spread of RSS . Similarly, mass-market distributors like Blockbuster may be threatened by distributors like LoveFilm , which supply the titles that Blockbuster doesn't offer because they are not already very popular. Some of the most successful Internet businesses have used

10795-494: The epitome of cool)". An article by Melissa Bell of The Washington Post posed the question: "Malcolm Gladwell: Bank of America's new spokesman?" Mother Jones editor Clara Jeffery said Gladwell's job for Bank of America had "terrible ethical optics". However, Gladwell says he was unaware that Bank of America was "bragging about his speaking engagements" until the Atlantic Wire emailed him. Gladwell explained: I did

10922-492: The final chapter of Outliers, "impervious to all forms of critical thinking" and said Gladwell believes "a perfect anecdote proves a fatuous rule". Gladwell has also been criticized for his emphasis on anecdotal evidence over research to support his conclusions. Maureen Tkacik and Steven Pinker have challenged the integrity of Gladwell's approach. Even while praising Gladwell's writing style and content, Pinker summed up Gladwell as "a minor genius who unwittingly demonstrates

11049-403: The first 20% of items in the distribution. 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

11176-457: The graph shown above, Amazon's book sales would be represented along the vertical axis, while the book or movie ranks are along the horizontal axis. The total volume of low popularity items exceeds the volume of high popularity items. Erik Brynjolfsson , Yu (Jeffrey) Hu , and Michael D. Smith found that a large proportion of Amazon.com 's book sales come from obscure books that were not available in brick-and-mortar stores. They then quantified

11303-481: The hazards of statistical reasoning", while accusing him of "cherry-picked anecdotes, post-hoc sophistry and false dichotomies" in his book Outliers . Referencing a Gladwell reporting mistake in which Gladwell refers to " eigenvalue " as "Igon Value", Pinker criticizes his lack of expertise: "I will call this the Igon Value Problem: when a writer's education on a topic consists in interviewing an expert, he

11430-430: 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

11557-622: The intuitive interpretation for a right-tailed long-tailed distributed quantity that if the long-tailed quantity exceeds some high level, the probability approaches 1 that it will exceed any other higher level. All long-tailed distributions are heavy-tailed, but the converse is false, and it is possible to construct heavy-tailed distributions that are not long-tailed. Subexponentiality is defined in terms of convolutions of probability distributions . For two independent, identically distributed random variables X 1 , X 2 {\displaystyle X_{1},X_{2}} with

11684-404: The ladder, since they are more likely to take more credit for achievements and take less blame for failure. He states both that narcissists make the worst managers and that the system of rewarding "stars" eventually worsens a company's position. Gladwell states that the most successful long-term companies are those who reward experience above all else and require greater time for promotions. With

11811-474: The later statistics as a known uncertainty or a discrepancy value can be found in. Bootstrap is another tool to find smoothing parameters using approximations of unknown MSE by different schemes of re-samples selection, see e.g. Malcolm Gladwell Malcolm Timothy Gladwell CM (born 3 September 1963) is a Canadian journalist, author, and public speaker. He has been a staff writer for The New Yorker since 1996. He has published eight books. He

11938-436: The long tail also has implications for the producers of content, especially those whose products could not – for economic reasons – find a place in pre-Internet information distribution channels controlled by book publishers, record companies, movie studios, and television networks. Looked at from the producers' side, the long tail has made possible a flowering of creativity across all fields of human endeavour. One example of this

12065-708: The long tail as part of their business strategy. Examples include eBay (auctions), Yahoo! and Google (web search), Amazon (retail), and iTunes Store (music and podcasts ), amongst the major companies, along with smaller Internet companies like Audible (audio books) and LoveFilm (video rental). These purely digital retailers also have almost no marginal cost, which is benefiting the online services, unlike physical retailers that have fixed limits on their products. The internet can still sell physical goods, but at an unlimited selection and with reviews and recommendations. The internet has opened up larger territories to sell and provide its products without being confined to just

12192-499: The long tail formation of user choices. Consumers' reliance on online user reviews to choose products is significantly influenced by the quantity of products available. Specifically, they find that the impacts of both positive and negative user reviews are weakened as product variety goes up. In addition, the increase in product variety reduces the impact of user reviews on popular products more than it does on niche products. The "crowds" of customers, users and small companies that inhabit

12319-411: The long tail has grown longer over time, with niche books accounting for a larger share of total sales. Their analyses suggested that by 2008, niche books accounted for 36.7% of Amazon's sales while the consumer surplus generated by niche books has increased at least fivefold from 2000 to 2008. In addition, their new methodology finds that, while the widely used power laws are a good first approximation for

12446-436: The long tail opens up a large space for authentic works of creativity. Television is a good example of this: Chris Anderson defines long-tail TV in the context of "content that is not available through traditional distribution channels but could nevertheless find an audience." Thus, the advent of services such as television on demand , pay-per-view and even premium cable subscription services such as HBO and Showtime open up

12573-402: The long tail. 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,

12700-607: The long-tail distribution can perform collaborative and assignment work. Some relevant forms of these new production models are: The demand-side factors that lead to the long tail can be amplified by the "networks of products" which are created by hyperlinked recommendations across products. An MIS Quarterly article by Gal Oestreicher-Singer and Arun Sundararajan shows that categories of books on Amazon.com which are more central and thus influenced more by their recommendation network have significantly more pronounced long-tail distributions. Their data across 200 subject areas shows that

12827-556: The lowest common denominator, a long-tail model may lead to improvement in a society's level of culture. The opportunities that arise because of the long tail greatly affect society's cultures because suppliers have unlimited capabilities due to infinite storage and demands that were unable to be met prior to the long tail are realized. At the end of the long tail, the conventional profit-making business model ceases to exist; instead, people tend to come up with products for varied reasons like expression rather than monetary benefit. In this way,

12954-977: The maximum-likelihood estimator (MLE). With ( X n , n ≥ 1 ) {\displaystyle (X_{n},n\geq 1)} a random sequence of independent and same density function F ∈ D ( H ( ξ ) ) {\displaystyle F\in D(H(\xi ))} , the Maximum Attraction Domain of the generalized extreme value density H {\displaystyle H} , where ξ ∈ R {\displaystyle \xi \in \mathbb {R} } . If lim n → ∞ k ( n ) = ∞ {\displaystyle \lim _{n\to \infty }k(n)=\infty } and lim n → ∞ k ( n ) n = 0 {\displaystyle \lim _{n\to \infty }{\frac {k(n)}{n}}=0} , then

13081-624: The misconception seems to be that management and executives are all too ready to classify employees without ample performance records and thus make hasty decisions. Many companies believe in disproportionately rewarding "stars" over other employees with bonuses and promotions. However, with the quick rise of inexperienced workers with little in-depth performance review, promotions are often incorrectly made, putting employees into positions they should not have and keeping other, more experienced employees from rising. He also points out that under this system, narcissistic personality types are more likely to climb

13208-464: The most popular movies to ensure that no shelf space is wasted. Because online video rental provider (such as Amazon.com or Netflix ) stocks movies in centralized warehouses, its storage costs are far lower and its distribution costs are the same for a popular or unpopular movie. It is therefore able to build a viable business stocking a far wider range of movies than a traditional movie rental store. Those economics of storage and distribution then enable

13335-436: The opportunity for niche content to reach the right audiences, in an otherwise mass medium. These may not always attract the highest level of viewership, but their business distribution models make that of less importance. As the opportunity cost goes down, the choice of TV programs grows and greater cultural diversity rises. Often presented as a phenomenon of interest primarily to mass market retailers and web-based businesses,

13462-464: The optimal inventory may in many cases be less than the millions of items that they can potentially offer. In other words, by proceeding further and further into the long tail, sales may become so small that the marginal cost of tracking them in rank order, even at a digital scale, might be optimised well before a million titles, and certainly before infinite titles. This model can provide further predictions into markets with long-tail distribution, such as

13589-438: The podcast Revisionist History , initially produced through Panoply Media and now through Gladwell's own podcast company. It began in 2016 and has aired seven 10-episode seasons. Each episode begins with an inquiry about a person, event, or idea, and proceeds to question the received wisdom about the subject. Gladwell was recruited to create a podcast by Jacob Weisberg , editor-in-chief of The Slate Group , which also includes

13716-548: The podcast network Panoply Media. In September 2018, Gladwell announced he was co-founding a podcast company, later named Pushkin Industries , with Weisberg. About this decision, Gladwell told the Los Angeles Times : "There is a certain kind of whimsy and emotionality that can only be captured on audio." He also has a music podcast with Bruce Headlam and Rick Rubin , titled Broken Record where they interview musicians. It has two seasons, 2018–2019 and 2020 with

13843-501: The potential value of the long tail to consumers. In an article published in 2003, these authors showed that, while most of the discussion about the value of the Internet to consumers has revolved around lower prices, consumer benefit (a.k.a. consumer surplus ) from access to increased product variety in online book stores is ten times larger than their benefit from access to lower prices online. A subsequent study by Erik Brynjolfsson , Yu (Jeffrey) Hu , and Michael D. Smith found that

13970-413: The power of collaborative innovation and stay ahead of the competition. Ultimately, involving users in the innovation process is a win-win for both companies and their customers, as it leads to more tailored, effective products and services that better meet the needs of the end user. The drive to build a market and obtain revenue from the consumer demographic of the long tail has led businesses to implement

14097-441: The rank-sales relationship, the slope may not be constant for all book ranks, with the slope becoming progressively steeper for more obscure books. In support of their findings, Wenqi Zhou and Wenjing Duan not only find a longer tail but also a fatter tail by an in-depth analysis on consumer software downloading pattern in their paper "Online user reviews, product variety, and the long tail". The demand for all products decreases, but

14224-592: The release of The Bomber Mafia: A Dream, a Temptation, and the Longest Night of the Second World War in April 2021, Gladwell has had seven books published. When asked for the process behind his writing, he said: "I have two parallel things I'm interested in. One is, I'm interested in collecting interesting stories, and the other is I'm interested in collecting interesting research. What I'm looking for

14351-408: The same thing—strangers misunderstanding each other." It challenges the assumptions we are programmed to make when encountering strangers, and the potentially dangerous consequences of misreading people we do not know. Gladwell's seventh book, The Bomber Mafia: A Dream, a Temptation, and the Longest Night of the Second World War , was released in April 2021. The book weaves together the stories of

14478-538: The scientific method." In that regard, The New Republic has called him "America's Best-Paid Fairy-Tale Writer". His approach was satirized by the online site "The Malcolm Gladwell Book Generator". In 2005, Gladwell commanded a $ 45,000 speaking fee. In 2008, he was making "about 30 speeches a year—most for tens of thousands of dollars, some for free", according to a profile in New York magazine. In 2011, he gave three talks to groups of small businessmen as part of

14605-580: The second highest honour for merit in the system of orders, decorations, and medals of Canada . He has received honorary degrees from the University of Waterloo (2007) and the University of Toronto (2011). Gladwell was a featured storyteller for the Moth podcast. He told a story about a well-intentioned wedding toast for a young man and his friends that went wrong. Gladwell was featured in General Motors "EVerybody in." campaign. Gladwell

14732-627: The standard bank or credit card customer. It also is a business model that fills an important developmental role in an economy. Grameen Bank in Bangladesh has successfully followed this business model. In Mexico the banks Compartamos and Banco Azteca also service this customer demographic, with an emphasis on consumer credit. Kiva.org is an organization that provides micro credits to people worldwide, by using intermediaries called small microfinance organizations (S.M.O.'s)to distribute crowd sourced donations made by Kiva.org lenders. According to

14859-400: The subexponential class, introduced by Jozef Teugels . There is still some discrepancy over the use of the term heavy-tailed . There are two other definitions in use. Some authors use the term to refer to those distributions which do not have all their power moments finite; and some others to those distributions that do not have a finite variance . The definition given in this article

14986-576: The trend of American parents " redshirting " their five-year-olds (postponing entrance into kindergarten to give them an advantage) to a section in Gladwell's Outliers . Sociology professor Shayne Lee referenced Outliers in a CNN editorial commemorating Martin Luther King Jr. 's birthday. Lee discussed the strategic timing of King's ascent from a "Gladwellian perspective". Gladwell gives credit to Richard Nisbett and Lee Ross for inventing

15113-468: The two books had sold a combined 4.5 million copies. Gladwell's third book, Outliers , published in 2008, examines how a person's environment, in conjunction with personal drive and motivation, affects his or her possibility and opportunity for success. Gladwell's original question revolved around lawyers: "We take it for granted that there's this guy in New York who's the corporate lawyer, right? I just

15240-446: The user-led innovation model in his book Democratizing Innovation . Among his conclusions is the insight that as innovation becomes more user-centered the information needs to flow freely, in a more democratic way, creating a "rich intellectual commons" and "attacking a major structure of the social division of labor". In today's world, customers are eager to voice their opinions and shape the products and services they use. This presents

15367-447: The world through the eyes of others, even if that other happens to be a dog. Gladwell's fifth book, David and Goliath , was released in October 2013, and examines the struggle of underdogs versus favourites. The book is partially inspired by an article Gladwell wrote for The New Yorker in 2009 entitled "How David Beats Goliath". The book was a bestseller but received mixed reviews. Gladwell's sixth book, Talking to Strangers ,

15494-486: The young Tom Wolfe." Farhad Manjoo at Salon described the book as "a real pleasure. As in the best of Gladwell's work, Blink brims with surprising insights about our world and ourselves." The Economist called Outliers "a compelling read with an important message". David Leonhardt wrote in The New York Times Book Review : "In the vast world of nonfiction writing, Malcolm Gladwell

15621-402: Was a Jamaican free woman of colour (mixed black and white) who was a slaveowner. His great-great-great-grandmother was of Igbo ethnicity from Nigeria. In the epilogue of his 2008 book Outliers he describes many lucky circumstances that came to his family over the course of several generations, contributing to his path towards success. Gladwell has said that his mother is his role model as

15748-400: Was argued to create a societal surplus of peace, a reservoir that can be mobilized in case a state needs it. The long tail thus functionally resembles " weak ties " in interpersonal networks. Before a long tail works, only the most popular products are generally offered. When the cost of inventory storage and distribution fall, a wide range of products become available. This can, in turn, have

15875-503: Was curious: Why is it all the same guy?", referring to the fact that "a surprising number of the most powerful and successful corporate lawyers in New York City have almost the exact same biography". In another example given in the book, Gladwell noticed that people ascribe Bill Gates 's success to being "really smart" or "really ambitious". He noted that he knew a lot of people who are really smart and really ambitious, but not worth $ 60 billion. "It struck me that our understanding of success

16002-562: Was really crude—and there was an opportunity to dig down and come up with a better set of explanations." Gladwell's fourth book, What the Dog Saw: And Other Adventures , was published in 2009. What the Dog Saw bundles together Gladwell's favourites of his articles from The New Yorker since he joined the magazine as a staff writer in 1996. The stories share a common theme, namely that Gladwell tries to show us

16129-477: Was released September 2019. The book examines interactions with strangers, covers examples that include the deceptions of Bernie Madoff , the trial of Amanda Knox , the suicide of Sylvia Plath , the Jerry Sandusky pedophilia case at Penn State , and the death of Sandra Bland . Gladwell explained what inspired him to write the book as being "struck by how many high profile cases in the news were about

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