Neal Becker wrote: > 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}
That's currently what's implemented, but there is simply no evidence that anyone ever uses this definition for complex random variables. Note that for real variables, E{(x-E[x])^2} = E{|x-E[x]|^2} but for complex variables, there is a large difference. Since the || are superfluous with real variables, probability texts rarely include them unless if they are then going on to talk about complex variables. If you want to extend the definition for real variables to complex variables, that is an ambiguity you have to resolve. There is, apparently, a large body of statistical signal processing literature that defines the complex variance as E{|z-E[z]|^2} so, I (now) believe that this is what should be implemented. -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion