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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 22, 2013 9:12 AM

On 22/02/2013 0:52, Rich Ulrich wrote:
> On Thu, 21 Feb 2013 20:54:44 +0100, Cristiano <cristiapi@NSgmail.com>
> wrote:
>

>> 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

>
>
> CAREFUL. You stated a problem about the uniform. You are

I know how to exactly calculate the confidence interval for the normal
distribution, so I use the exact confidence interval to check my
simulation. I'd say that it is relevant! :-)

>> 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.

>>
>> 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.

>
> When you are looking at one tail only, the matter of symmetry does
> not arise. You stated your tentative solution as just one percentile.
> The difficulty of asymmetry does not arise for one limit alone.

Then there should be something wrong in my simulation, because I get a
totally wrong result for the one-sided CI of the SD for the normal

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