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Re: Simulation for the standard deviation
Posted:
Feb 26, 2013 9:04 PM
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"Cristiano" wrote in message news:kgjnqn$tvp$1@dont-email.me...
On 26/02/2013 1:56, David Jones wrote:
> The standard work, Kendall & Stuart's "Theoretical Statistics" will
> provide a formula for variance of the sample variance. This could be
> used to provide a sampling interval for the sample variance, and hence
> for the sample standard deviation. Indeed, a formula for the variance of
> the sample variance exists on the Wikipedia page for "Variance".
>
> In the present context, an alternative is just to do multiple
> simulations of the sample standard deviation and use this to get the
> sampling distribution empirically. Of course this would assume that the
> random number generator has adequate properties.
In my simulations I use the (very good and very fast) dSFMT generator
and I get, for example, with n= 2, E[s^2]= .0833584 (good) and Var[s^2]=
.00972501.
Using the formula given here:
http://en.wikipedia.org/wiki/Variance#Distribution_of_the_sample_variance
I get: Var[s^2]= .00369776.
Using the formula given here:
http://mathworld.wolfram.com/SampleVarianceDistribution.html
I get: Var[s^2]= .000924963.
Where is the error?
Cristiano
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"Wolfram" is using a definition of sample variance with a divisor "N", the
sample size: "Wikipedia" is using the more standard definition of sample
variance with a divisor "N-1". This explains the ratio of 4 between the 2
answers. You need to check which version you have programmed and which you
actually want.
David Jones
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