[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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