Excess kurtosis Kurtosis

1 excess kurtosis

1.1 mesokurtic
1.2 leptokurtic
1.3 platykurtic

excess kurtosis

the excess kurtosis defined kurtosis minus 3. there 3 distinct regimes described below.

mesokurtic

distributions 0 excess kurtosis called mesokurtic, or mesokurtotic. prominent example of mesokurtic distribution normal distribution family, regardless of values of parameters. few other well-known distributions can mesokurtic, depending on parameter values: example, binomial distribution mesokurtic



p
=
1

/

2
±


1

/

12




{\displaystyle p=1/2\pm {\sqrt {1/12}}}

.

leptokurtic

a distribution positive excess kurtosis called leptokurtic, or leptokurtotic. lepto- means slender . in terms of shape, leptokurtic distribution has fatter tails. examples of leptokurtic distributions include student s t-distribution, rayleigh distribution, laplace distribution, exponential distribution, poisson distribution , logistic distribution. such distributions termed super-gaussian.

platykurtic

the coin toss platykurtic distribution

a distribution negative excess kurtosis called platykurtic, or platykurtotic. platy- means broad . in terms of shape, platykurtic distribution has thinner tails. examples of platykurtic distributions include continuous or discrete uniform distributions, , raised cosine distribution. platykurtic distribution of bernoulli distribution p = ½ (for example number of times 1 obtains heads when flipping coin once, coin toss), excess kurtosis −2. such distributions termed sub-gaussian.