kurtosis (Statistics Toolbox)

Sample kurtosis.

Syntax

k = kurtosis(X)

Description

k = kurtosis(X) returns the sample kurtosis of X. For vectors,
kurtosis(x) is the kurtosis of the elements in the vector, x. For matrices kurtosis(X) returns the sample kurtosis for each column of X.

Kurtosis is a measure of how outlier-prone a distribution is. The kurtosis of the normal distribution is 3. Distributions that are more outlier-prone than the normal distribution have kurtosis greater than 3; distributions that are less outlier-prone have kurtosis less than 3.

The kurtosis of a distribution is defined as

where E(x) is the expected value of x.

Note: Some definitions of kurtosis subtract 3 from the computed value, so that the normal distribution has kurtosis of 0. The kurtosis function does not use this convention.

Example

X = randn([5 4])

X =

    1.1650    1.6961   -1.4462   -0.3600
    0.6268    0.0591   -0.7012   -0.1356
    0.0751    1.7971    1.2460   -1.3493
    0.3516    0.2641   -0.6390   -1.2704
   -0.6965    0.8717    0.5774    0.9846

k = kurtosis(X)

k =

    2.1658    1.2967    1.6378    1.9589