0
$\begingroup$

Is there a direct command in Mathematica that computes the covariance between two random variables?

Hence, instead of typing 

Expectation[f(x)*g(y),{y~some distribution,x~some distribution}] - 
Expectation[f(x),{y~some distribution,x~some distribution}]*
Expectation[g(y),{y~some distribution,x~some distribution}]

Is there a command that archieves the same by typing simply

Covariance[{f(x),g(y)},{y~some distribution,x~some distribution}]

I have tried to use the following function:

CoVar[RVfuncs_, dist_] := 
Expectation[RVfuncs[[1]]*RVfuncs[[2]], 
dist] - (Expectation[RVfuncs[[1]], dist]*Expectation[RVfuncs[[2]], dist])

It works, but it is much slower than writing out the three "Expectation" parts.

Improve this question
$\endgroup$
5
  • $\begingroup$ The covariance between 2 random variables whose distributions are specified as in your examples will always be 0. You need to specify a multivariate distribution, such as Covariance[BinormalDistribution[{m1, m2}, {sd1, sd2}, corr], 1, 2] $\endgroup$
    – Rojo
    Oct 31, 2013 at 16:27
  • $\begingroup$ How about the case x = y $\endgroup$
    – Breugem
    Oct 31, 2013 at 16:33
  • $\begingroup$ I don't understand what you mean. If you tell Mathematica that {x~someDist, y~someDist}, it assumes they are independent, so unless someDist is a delta, you don't get x=y, and in such case I would think the covariance is indeterminate $\endgroup$
    – Rojo
    Oct 31, 2013 at 16:43
  • $\begingroup$ About your edit and your CoVar function, what exactly is slower? $\endgroup$
    – Rojo
    Oct 31, 2013 at 16:44
  • $\begingroup$ Ok thanks I see your point. I will rephrase the question $\endgroup$
    – Breugem
    Oct 31, 2013 at 16:45

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.