Date: Dec 27, 2012 7:03 AM
Subject: Binomial variance for DFT
I have n/2 real numbers.
I calculate a threshold T (a real number) for which p * n/2 numbers (0 <
p < 1) are expected to fall below T.
Then I count how many numbers are less than T.
That count should have a binomial distribution, right? Hence, its
variance should be
n/2 * p * (1-p).
But the n/2 numbers are the modulus of the first n/2 complex numbers
obtained from a discrete Fourier transform and the variance should be
n/2 * p * (1-p) / 2
as explained here (page 10):
Unfortunately, the value given in the paper is significantly different
from the one obtained by extensive simulations.
Does anybody now a procedure or a formula to calculate the exact
variance of the counts?