Editing Kurtosis (section)

== Excess kurtosis ==
The ''excess kurtosis'' is defined as kurtosis minus 3. There are 3 distinct regimes as described below.

=== Mesokurtic ===
Distributions with zero excess kurtosis are called '''mesokurtic''', or '''mesokurtotic'''. The most prominent example of a mesokurtic distribution is the normal distribution family, regardless of the values of its [[parameter]]s. A few other well-known distributions can be mesokurtic, depending on parameter values: for example, the [[binomial distribution]] is mesokurtic for <math display="inline">p = 1/2 \pm \sqrt{1/12}</math>.

=== Leptokurtic ===
A distribution with [[Positive number|positive]] excess kurtosis is called '''leptokurtic''', or '''leptokurtotic'''. "Lepto-" means "slender".<ref>{{Cite web | url=http://medical-dictionary.thefreedictionary.com/lepto- | title=Lepto-}}</ref> A leptokurtic distribution has ''[[Fat-tailed distribution|fatter tails]]''. Examples of leptokurtic distributions include the [[Student's t-distribution]], [[Rayleigh distribution]],  [[Laplace distribution]], [[exponential distribution]], [[Poisson distribution]] and the [[logistic distribution]].  Such distributions are sometimes termed ''super-Gaussian''.{{r|Beneviste1980}}
[[File:Three probability density functions.png|thumb|Three symmetric increasingly leptokurtic probability density functions; their intersections are indicated by vertical lines.]]

=== Platykurtic ===
[[File:1909 US Penny.jpg|thumb|The [[coin toss]] is the most platykurtic distribution]]
A distribution with [[Negative number|negative]] excess kurtosis is called '''platykurtic''', or '''platykurtotic'''. "Platy-" means "broad".<ref>{{cite web| url = http://www.yourdictionary.com/platy-prefix| url-status = dead| archive-url = https://web.archive.org/web/20071020202653/http://www.yourdictionary.com/platy-prefix| archive-date = 2007-10-20| title = platy-: definition, usage and pronunciation - YourDictionary.com}}</ref> A platykurtic distribution has ''thinner tails''. Examples of platykurtic distributions include the [[Continuous uniform distribution|continuous]] and [[discrete uniform distribution]]s, and the [[raised cosine distribution]]. The most platykurtic distribution of all is the [[Bernoulli distribution]] with ''p'' = 1/2 (for example the number of times one obtains "heads" when flipping a coin once, a [[coin toss]]), for which the excess kurtosis is −2.