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The fat tail is a phenomenon of approximately normal probability distributions that emerge in practice; that is, in the real world. According to the theoretical distribution, events that deviate from the mean by five or more standard deviations ("5-sigma event") are extremely rare, with 10- or more sigma being practically impossible. However, under many applications, such events are more common than expected; 15- or more sigma events have happened in finance, for example. Because the real-world commonality of high-sigma events is much greater than in theory, the distribution is "fatter" at the extremes ("tails") than a truly normal one. Wikipedia does not have an article with this exact name. ... It has been suggested that this article or section be merged with The long tail. ... The normal distribution, also called Gaussian distribution (although Gauss was not the first to work with it), is an extremely important probability distribution in many fields. ... In mathematics and statistics, a probability distribution, more properly called a probability density, assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... In statistics, mean has two related meanings: the average in ordinary English, which is also called the arithmetic mean (and is distinguished from the geometric mean or harmonic mean). ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is defined as the square root of the variance. ... Finance studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. ...

In finance, fat tails are considered undesirable because of the additional risk they introduce. For example, an investment strategy may have an expected return, after one year, that is five times its standard deviation. Assuming a normal distribution, the likelihood of its failure (negative return) is less than one in a million; in practice, it may be higher. Normal distributions that emerge in finance generally do so because the factors influencing an asset's value or price are mathematically "well-behaved", and the central limit theorem provides for such a distribution. However, traumatic "real-world" events (such as an oil shock, a large corporate bankruptcy, or an abrupt change in a political situation) are usually not mathematically well-behaved. To meet Wikipedias quality standards, this article may require cleanup. ... A central limit theorem is any of a set of weak-convergence results in probability theory. ... An Energy Crisis is any great shortfall (or price rise) in the supply of energy to an economy. ...

To understand why this phenomenon may occur, consider the following: Any assessment with a finite ceiling (such as an IQ test, whereas someone's measured weight isn't theoretically finite) will award its maximum score to anyone who earns it. However, a portion of the people awarded the highest score would have achieved higher if it were possible. All of these people with the same "max" score results in a greater than expected frequency. The same applies on the low end of a normal curve.