R: Kurtosis

kurtosis {e1071} | R Documentation

## Kurtosis

### Description

Computes the kurtosis.

### Usage

    kurtosis(x, na.rm = FALSE, type = 3)

### Arguments

`x` | a numeric vector containing the values whose kurtosis is to be computed.
`na.rm` | a logical value indicating whether `NA` values should be stripped before the computation proceeds.
`type` | an integer between 1 and 3 selecting one of the algorithms for computing kurtosis detailed below.

### Details

If `x` contains missings and these are not removed, the kurtosis is `NA`.

Otherwise, write x_i for the non-missing elements of `x`, n for their number, mu for their mean, s for their standard deviation, and m_r = ∑_i (x_i - mu)^r / n for the sample moments of order r.

Joanes and Gill (1998) discuss three methods for estimating kurtosis:

Type 1:

  g_2 = m_4 / m_2^2 - 3. This is the typical definition used in many older textbooks.

Type 2:

  G_2 = ((n+1) g_2 + 6) * (n-1) / ((n-2)(n-3)). Used in SAS and SPSS.

Type 3:

  b_2 = m_4 / s^4 - 3 = (g_2 + 3) (1 - 1/n)^2 - 3. Used in MINITAB and BMDP.

Only G_2 (corresponding to `type = 2`) is unbiased under normality.

### Value

The estimated kurtosis of `x`.

### References

D. N. Joanes and C. A. Gill (1998), Comparing measures of sample skewness and kurtosis. The Statistician, 47, 183–189.

### Examples

    x <- rnorm(100)
    kurtosis(x)

[Package e1071 version 1.7-6 Index]