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

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 Ray Koopman Posts: 3,383 Registered: 12/7/04
Re: Simulation for the standard deviation
Posted: Feb 28, 2013 6:28 PM
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On Feb 28, 10:51 am, Cristiano <cristi...@NSgmail.com> wrote:
>
> 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.

Last night I found the cdf of s for n = 3.
Perhaps someone can simplify it.
I[#] = 1 or 0 according as # is true or false.

n = 2: 0 <= s <= sqrt(1/2)

F(s) = 2s (sqrt(2) - s)

n = 3: 0 <= s <= sqrt(1/3)

F(s) = sqrt(3)*( 2s^2 (pi - 4s) + I[s > 1/2]*
( t + 4s^2 (2t - 3 arctan t) ) ),

where t = sqrt(4s^2 - 1).

Don't hold your breath waiting for n > 3.

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

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