
Re: Simulation for the standard deviation
Posted:
Feb 21, 2013 2:54 PM


On 21/02/2013 6:46, Rich Ulrich wrote: > On Wed, 20 Feb 2013 12:54:26 +0100, Cristiano <cristiapi@NSgmail.com> > wrote: > >> Short question: does anybody know how to calculate the confidence >> interval of the standard deviation for the uniform distribution? >> >> >> Long version. >> >> From a population of iid real numbers (double precision C++ type) I >> randomly pick many numbers with replacement and I calculate the standard >> deviation of those numbers. >> >> I repeat many times the above procedure to obtain many values of the >> standard deviation. >> >> Then, I calculate the 10th percentile of the standard deviations. >> >> What's that percentile? I'm aware that it's not a confidence limit. >> How do I calculate the CI via simulation? >> > > I think I would call it a Monte Carlo estimate of the onesided CI.
To check my simulation, I calculated the CI for the normal distribution as explained here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc231.htm
For example, for N(0,1), when N= 60 and alpha= 0.01, I get: 0.806465 <= sigma <= 1.30263 (twosided) and 0.822722 <= sigma, 0 <= sigma <= 1.26795
while the simulation converges to 0.7885 <= sigma.
> Assuming that you are describing a recommended procedure for > bootstrapping, that seems like the way to simulate that CI.
I found this link: http://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29#Deriving_confidence_intervals_from_the_bootstrap_distribution and I think that I'm using the "Percentile Bootstrap".
There is an interesting phrase: "This method can be applied to any statistic. It will work well in cases where the bootstrap distribution is symmetrical and centered on the observed statistic [...]".
The reason of my wrong result could be that the bootstrap distribution of the standard deviation is not symmetrical, I guess.
> You could assume that the mean is known (since it is) and > calculate the SDs while dividing by N instead of N1, using > that mean.
I know both the mean and the standard deviation (of the population) because I use real numbers in N(0,1) or U(0,1).
Cristiano

