Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.stat.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Cristiano

Posts: 36
Registered: 12/7/12
Re: Simulation for the standard deviation
Posted: Feb 26, 2013 8:36 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 26/02/2013 1:56, David Jones wrote:
> The standard work, Kendall & Stuart's "Theoretical Statistics" will
> provide a formula for variance of the sample variance. This could be
> used to provide a sampling interval for the sample variance, and hence
> for the sample standard deviation. Indeed, a formula for the variance of
> the sample variance exists on the Wikipedia page for "Variance".
>
> In the present context, an alternative is just to do multiple
> simulations of the sample standard deviation and use this to get the
> sampling distribution empirically. Of course this would assume that the
> random number generator has adequate properties.


In my simulations I use the (very good and very fast) dSFMT generator
and I get, for example, with n= 2, E[s^2]= .0833584 (good) and Var[s^2]=
.00972501.

Using the formula given here:
http://en.wikipedia.org/wiki/Variance#Distribution_of_the_sample_variance
I get: Var[s^2]= .00369776.

Using the formula given here:
http://mathworld.wolfram.com/SampleVarianceDistribution.html
I get: Var[s^2]= .000924963.

Where is the error?

Cristiano



Date Subject Author
2/20/13
Read Simulation for the standard deviation
Cristiano
2/21/13
Read Re: Simulation for the standard deviation
Richard Ulrich
2/21/13
Read Re: Simulation for the standard deviation
Cristiano
2/21/13
Read Re: Simulation for the standard deviation
Richard Ulrich
2/22/13
Read Re: Simulation for the standard deviation
Cristiano
2/22/13
Read Re: Simulation for the standard deviation
Richard Ulrich
2/21/13
Read Re: Simulation for the standard deviation
Ray Koopman
2/22/13
Read Re: Simulation for the standard deviation
Ray Koopman
2/22/13
Read Re: Simulation for the standard deviation
Cristiano
2/22/13
Read Re: Simulation for the standard deviation
Ray Koopman
2/23/13
Read Re: Simulation for the standard deviation
Cristiano
2/23/13
Read Re: Simulation for the standard deviation
Ray Koopman
2/23/13
Read Re: Simulation for the standard deviation
Cristiano
2/24/13
Read Re: Simulation for the standard deviation
Cristiano
2/24/13
Read Re: Simulation for the standard deviation
Ray Koopman
2/24/13
Read Re: Simulation for the standard deviation
Cristiano
2/25/13
Read Re: Simulation for the standard deviation
Ray Koopman
2/25/13
Read Re: Simulation for the standard deviation
Cristiano
2/25/13
Read Re: Simulation for the standard deviation
Ray Koopman
2/25/13
Read Re: Simulation for the standard deviation
David Jones
2/26/13
Read Re: Simulation for the standard deviation
Cristiano
2/26/13
Read Re: Simulation for the standard deviation
David Jones
2/27/13
Read Re: Simulation for the standard deviation
Ray Koopman
2/27/13
Read Re: Simulation for the standard deviation
Cristiano
2/28/13
Read Re: Simulation for the standard deviation
Ray Koopman
2/28/13
Read Re: Simulation for the standard deviation
Cristiano
2/28/13
Read Re: Simulation for the standard deviation
Ray Koopman
3/1/13
Read Re: Simulation for the standard deviation
Cristiano

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.