R help - Jul 1999 - skewness, kurtosis

>>>>> On Wed, 28 Jul 1999 10:57:25 CET (+0100),
>>>>> Wolfgang Koller (WK) wrote:
WK> Dear R-Users and Developpers,
WK> Currently R does not include functions to compute the skewness and 
WK> kurtosis. I programmed it myself in the following way, but probably 
WK> *real* programmers/statisticians can do that better:

The package e1071 (available at CRAN) contains some statistical
functions we find useful, including our versions of skewness and
kurtosis. (They are more or less the same as your functions, besides
an additional na.rm-flag).

WK> mykurtosis <- function(x) {  
WK> m4 <- mean((x-mean(x))^4) 
WK> kurt <- m4/(sd(x)^4)-3  
WK> kurt
WK> }

WK> myskewness <-  function(x) {
WK> m3 <- mean((x-mean(x))^3)
WK> skew <- m3/(sd(x)^3)
WK> skew
WK> }

-aw

************************************************************************
*                          Andreas Weingessel                          *
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Dear R-Users and Developpers,

Currently R does not include functions to compute the skewness and 
kurtosis. I programmed it myself in the following way, but probably 
*real* programmers/statisticians can do that better:
 
mykurtosis <- function(x) {  
m4 <- mean((x-mean(x))^4) 
kurt <- m4/(sd(x)^4)-3  
kurt
}

myskewness <-  function(x) {
m3 <- mean((x-mean(x))^3)
skew <- m3/(sd(x)^3)
skew
}

I would also suggest to include the quartile-coefficient of skewness 
(sorry if this translation from German is not correct). This measure 
is confined to the interval [0,1] and much easier to interpret. 
My try:

myqcskewness <-  function(x) {
  x25 <- as.double(quantile(x,prob=0.25))
  x75 <- as.double(quantile(x,prob=0.75))
  qcsk <- (x25+x75-2*mean(x))/(x75-x25)
  qcsk
}

Finally a question which actually is not R-related (please excuse 
this misuse of the list):
Is there something like a "quantile-coefficient of kurtosis"??
 Maybe:
k = (2b-a)/a  with   a = x_{p} - x_{1-p},   b = x_{q} - x_{1-q},
x_{} are quantiles, and p and q are chosen so that k=0 for the normal 
distribution.

Thanks for help!!

WK


----------------------------------------------------------
Wolfgang Koller,  koller2 at fgr.wu-wien.ac.at
Research Institute for European Affairs
Vienna University of Economics and Business Administration
Althanstrasse 39-45, 1090 Vienna, Austria
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