Rolf Turner wrote: > On 28/03/2010, at 11:50 AM, Ben Bolker wrote: > >> Gang Chen <gangchen6 <at> gmail.com> writes: >> >>> Anybody knows what functions can be used to calculate >>> variance/covariance with complex numbers? var and cov don't seem to >>> work: >> How about: >> >> y <- complex(real=5:1,imag=2:6) >> z <- complex(real=1:5,imag=6:10) >> >> complex.var <- function(x) { >> mx <- mean(x) >> n <- length(x) >> mean((x-mx)^2)*n/(n-1) >> } > > <SNIP> > > Don't you want variances to be positive (non-negative) reals? > > IIRC the population variance of a complex random variable is > > E(|X - mu|^2) not E((X - mu)^2) > > So shouldn't your complex.var function have Mod(x-mx)^2 where > you currently have (x-mx)^2 ??? > > cheers, > > Rolf
Probably. To be honest, I wasn't thinking about it that carefully. It crossed my mind to wonder what the appropriate definition was of the variance for complex numbers, but I didn't bother to go find out. I guess it goes to show (yet again) that advice may be worth what you pay for it ... cheers Ben
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