R help - Dec 2005 - about comparison of KURTOSIS in package: moments and fBasics

Hello



I do not know very much about statistics (and English language too :-( ),
then I come in search of a clarification (explanation):

I found two distinct results on KURTOSIS and
I do not know which of them is the correct one.
Any aid will be welcome!


klebyn



################  CODE

rnorm(1000) -> x

library(moments)

kurtosis(x)
skewness(x)

detach("package:moments")
library(fBasics)

kurtosis(x)
skewness(x)

detach("package:fBasics")

R.version

################  OUTPUT

 >
 > rnorm(1000) -> x
 >
 >
 > library(moments)
 >
 >
 > kurtosis(x)
[1] 3.145274
 > skewness(x)
[1] 0.04898635
 >
 >
 > detach("package:moments")
 > library(fBasics)

Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
fBasics: Markets, Basic Statistics, Hypothesis Testing
 >
 >
 > kurtosis(x)
[1] 0.1389865
 > skewness(x)
[1] 0.04891289
 >
 >
 > detach("package:fBasics")
 >
 > R.version
         _              
platform i386-pc-mingw32
arch     i386           
os       mingw32        
system   i386, mingw32  
status                  
major    2              
minor    2.0            
year     2005           
month    10             
day      06             
svn rev  35749          
language R              
 >
 >

(Haven't seen an anwer to this yet; maybe I missed it.)

klebyn wrote:
> 
> 
> Hello
> 
> 
> 
> I do not know very much about statistics (and English language too :-( ),
> then I come in search of a clarification (explanation):
> 
> I found two distinct results on KURTOSIS and
> I do not know which of them is the correct one.
> Any aid will be welcome!
> 
> 
> klebyn
The code will show you why you get different results.

fBasics:
  kurtosis = sum((x - mean(x))^4/var(x)^2)/length(x) - 3

moments:
  n <- length(x)
  n * sum((x - mean(x))^4)/(sum((x - mean(x))^2)^2)

So pkg:moments uses the ratio of 4th sample moment to
square of second sample moment, while pkg:fBasics uses the
variance instead of the second moment and subtracts 3
(for reasons to do with the Normal distribution).


Peter Ehlers
> 
> 
> 
> ################  CODE
> 
> rnorm(1000) -> x
> 
> library(moments)
> 
> kurtosis(x)
> skewness(x)
> 
> detach("package:moments")
> library(fBasics)
> 
> kurtosis(x)
> skewness(x)
> 
> detach("package:fBasics")
> 
> R.version
> 
> ################  OUTPUT
> 
>  >
>  > rnorm(1000) -> x
>  >
>  >
>  > library(moments)
>  >
>  >
>  > kurtosis(x)
> [1] 3.145274
>  > skewness(x)
> [1] 0.04898635
>  >
>  >
>  > detach("package:moments")
>  > library(fBasics)
> 
> Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
> fBasics: Markets, Basic Statistics, Hypothesis Testing
>  >
>  >
>  > kurtosis(x)
> [1] 0.1389865
>  > skewness(x)
> [1] 0.04891289
>  >
>  >
>  > detach("package:fBasics")
>  >
>  > R.version
>          _              
> platform i386-pc-mingw32
> arch     i386           
> os       mingw32        
> system   i386, mingw32  
> status                  
> major    2              
> minor    2.0            
> year     2005           
> month    10             
> day      06             
> svn rev  35749          
> language R              
>  >
>  >
> 
> ______________________________________________
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> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html

Thanks to Spencer Graves for providing links to explain
the various types of kurtosis reported by R packages. 

Spencer Graves>>(http://mathworld.wolfram.com/k-Statistic.html).

Spencer also said:

SG>>	  However, these are little used, as the estimates are known to be so
SG>> highly variable.  It is generally preferred to transform to normality
or
SG>> to use some other distribution and then use maximum likelihood.

This advice is good if your interest is comparing models, but what 
if variation in kurtosis itself is your interest? I am wondering if 
someone could provide some direction for answering questions about 
differences between samples in kurtosis. There are tests of 
significance for means and variance. How would one test hypotheses 
of difference in kurtosis between samples? 

Thanks in advance. 

Harold Baize
Youth Services Evaluator
Butte County Department of Behavioral Health