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Re: Simulation for the standard deviation
Posted:
Feb 21, 2013 2:54 PM
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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 one-sided 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 (two-sided)
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
> boot-strapping, 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 N-1, 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
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