Re: [R] about comparison of KURTOSIS in package: moments and fBasics

From: P Ehlers <ehlers_at_math.ucalgary.ca>
Date: Sat 03 Dec 2005 - 09:28:26 EST

(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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R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sat Dec 03 11:21:30 2005

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