Kurtosis
Description
Computes the kurtosis.
Usage
1 
Arguments
x 
a numeric vector containing the values whose kurtosis is to be computed. 
na.rm 
a logical value indicating whether 
type 
an integer between 1 and 3 selecting one of the algorithms for computing skewness detailed below. 
Details
If x
contains missings and these are not removed, the skewness
is NA
.
Otherwise, write x_i for the nonmissing 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) * (n1) / ((n2)(n3)). 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
1 2 