[Numpy-discussion] def of var of complex
Neal Becker
ndbecker2@gmail....
Mon Jan 21 07:01:30 CST 2008
Neal Becker wrote:
> I noticed that if I generate complex rv i.i.d. with var=1, that numpy
> says:
>
> var (<real part>) -> (close to 1.0)
> var (<imag part>) -> (close to 1.0)
>
> but
>
> var (complex array) -> (close to complex 0)
>
> Is that not a strange definition?
I don't think there is any ambiguity about the definition of the variance of
complex.
Var(x) = E{(x-E[x])^2} = E{x}^2 - E{x}
An estimator for this:
E[x^n] \approx (1/M)\sum(x^n)
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