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Re: Simulation for the standard deviation
Posted:
Feb 28, 2013 1:51 PM
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On 28/02/2013 6:35, Ray Koopman wrote:
> On Feb 27, 5:13 am, Cristiano <cristi...@NSgmail.com> wrote:
>> On 27/02/2013 9:09, Ray Koopman wrote:
>>
>>> The variance of the unbiased sample variance in samples of size n
>>> from a Uniform(0,1) distribution is (2n+3)/(360n(n-1)). For n = 2
>>> this reduces to 7/720 = .0097222... .
>>
>> But how can I use that formula to calculate the p-value for
>> Var[s^2]? I should know the CDF of Var[s^2], right?
>
> You can get a p-value when n = 2, in which case sd = range/sqrt(2)
> and you can take advantage of the fact that we know the cdf of the
> range. Otherwise, unless someone can point you to the cdf of the sd
> (or, more likely, the variance), you'll have to get a Monte Carlo
> estimate of the p-value.
When one tries to use a Monte Carlo simulation to estimate a CDF, there
is the big problem of the tails: for small and big p-values, many
samples are needed.
I can get a very good estimate for p-values in the range, say, .001 < p
< .999, in a reasonable amount of time, but outside that range the
simulation starts to demand many numbers.
Cristiano
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