Re: var(x) and std(x)

[Michael Jachan]

Hi Anand!

This is not an error! There are 2 major ways to define estimators for 
variance (std. deviation). The one with 1/(N-1) as fore factor is an 
unbiased estimator, the other one is biassed with (N-1)/N. This follows 
from estimation theory, look into a good book about statistics to find 
out more...


Michael


Anand V wrote:

> Hi,
>   I have a doubt regarding the implementation of variance function var(x) in 
> octave.It finds the variance as follows
>
> function y = var(x)
>
>   if (nargin != 1)
>     usage ("var (x)");
>   endif
>
>   [nr, nc] = size (x);
>   if (nr == 0 || nc == 0)
>     error ("var: x must not be empty");
>   elseif ((nr == 1) && (nc == 1))
>     y = 0;
>   elseif ((nr == 1) || (nc == 1))
>     n = length (x);
>     y = (sumsq (x) - sum(x)^2 / n) / (n-1);
>   else
>     y = (sumsq (x) - sum(x).^2 / nr) / (nr-1);
>   endif
>
> endfunction
>
>    It gives variance after averaging over n-1 samples, rather than averaging over n samples. for example, if we calculate the variance of 
> x = [1,2,3] , it returns the value 1, instead of 2/3..This is because it
> finds 2/2 and not 2/3..The same is the case with std(x) also. 
> Is it an error or is there any explanation for that?
> Please correct me if I am wrong.
>
> Thanks and Regards
> Anand
>
>
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--
-----------------------------------------------------------
Michael Jachan
Institute of Communications and Radio-Frequency Engineering
Vienna University of Technology
A-1040 Vienna, Gusshausstr. 27/E389/111
address@hidden, ++43 1 58801 38914
www.nt.tuwien.ac.at/dspgroup/tfgroup/time.html



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Octave is freely available under the terms of the GNU GPL.

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