Re: Gaussian variance estimation

"David Delgado Gomez" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> Good morning,
>
> I have data with a normal distribution.  Values higher than the mean are
> corrupted with noise. Is it possible to estimate the variance of the
> gaussian distribution just taking into account values smaller than the
> mean?
> Thanks
> David
>

I have used Monte Carlo to look at the result of using the sum of squares of
deviations from the sample median.
I wanted to see if dividing by '(n-1)' as the number of degrees of freedom
is still appropriate.
What I found was interesting.   Sampling from a normal distribution and
using only deviations for the observations below the median, I found that
you should divide by (n/2) - 0.3 when n is even, and by ((n+1)/2) - 0.7 when
n is odd.
Here n is the total sample size.

My explanation of this difference between odd and even sample sizes is as
follows.
When n is even, the median is midway between two observations, so that the
smallest deviation from the median is only about half the size that it is
when n is even and the median is equal to the middle observation.

Cheers

-- 
Alan Miller
http://users.bigpond.net.au/amiller
Retired Statistician