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

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Sun 04 Dec 2005 - 03:06:49 EST

          Just a further point of clarification: W. E. Deming said there is no true value to any number obtained as a result of a measurement. If you change the method of measurement, you will tend to get different numbers. This introduces the theory of "operational definitions".

          The "correct" number for kurtosis depends on your purpose. The number for "kurtosis" that subtracts 3 estimates a "cumulant", which is the standard fourth moment correction weight in an Edgeworth expansion approximation to a distribution. Neither of the numbers described below compute the "4th sample k-statistic", which is "the unique unbiased estimator" for that number
(http://mathworld.wolfram.com/k-Statistic.html).

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

	  hope this helps.
	  spencer graves

P Ehlers wrote:

> (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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> 
> 
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-- 
Spencer Graves, PhD
Senior Development Engineer
PDF Solutions, Inc.
333 West San Carlos Street Suite 700
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spencer.graves@pdf.com
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Received on Sun Dec 04 03:13:58 2005

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