
Re: Simulation for the standard deviation
Posted:
Feb 28, 2013 6:28 PM


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 pvalues, > many samples are needed. > I can get a very good estimate for pvalues 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.

