
Re: Simulation for the standard deviation
Posted:
Feb 27, 2013 3:09 AM


On Feb 26, 5:36 pm, Cristiano <cristi...@NSgmail.com> wrote: > 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
The variance of the unbiased sample variance in samples of size n from a Uniform(0,1) distribution is (2n+3)/(360n(n1)). For n = 2 this reduces to 7/720 = .0097222... .

