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Topic: Simulation for the standard deviation
Replies: 27   Last Post: Mar 1, 2013 7:30 AM

 Messages: [ Previous | Next ]
 Cristiano Posts: 60 Registered: 12/7/12
Re: Simulation for the standard deviation
Posted: Feb 28, 2013 1:51 PM

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

Date Subject Author
2/20/13 Cristiano
2/21/13 Richard Ulrich
2/21/13 Cristiano
2/21/13 Richard Ulrich
2/22/13 Cristiano
2/22/13 Richard Ulrich
2/21/13 Ray Koopman
2/22/13 Ray Koopman
2/22/13 Cristiano
2/22/13 Ray Koopman
2/23/13 Cristiano
2/23/13 Ray Koopman
2/23/13 Cristiano
2/24/13 Cristiano
2/24/13 Ray Koopman
2/24/13 Cristiano
2/25/13 Ray Koopman
2/25/13 Cristiano
2/25/13 Ray Koopman
2/25/13 David Jones
2/26/13 Cristiano
2/26/13 David Jones
2/27/13 Ray Koopman
2/27/13 Cristiano
2/28/13 Ray Koopman
2/28/13 Cristiano
2/28/13 Ray Koopman
3/1/13 Cristiano