How about the following:
Suppose you have the bivariate cumulative distribution function
(cdf) for (X, Y).
1. From this first compute the marginal cdf for X. The median
will give you EX, and you can get sigmaX = IQR/(2*qnorm(0.75)), where
IQR = interquartile range = diff(quantile(..., c(0.25, 0.75))). Repeat
to get EY and sigmaY.
2. Next compute the median of the conditional distribution for Y
given X = (EX+sigmaX). This is E(Y|X=EX+sigmaX) = EY+rho*sigmaY. [The
regression equation is E(Y|x) = EY + rho*(x-EX)*sigmaY/sigmaX, and
(x-EX) = sigmaX by choice.] From this, you can now solve for rho. You
may also wish to repeat this for EX-sigmaX as a check.
If you have trouble translating this into R code, please make an
attempt, then read the posting guide
"http://www.R-project.org/posting-guide.html", and prepare a follow-up
question as needed. (In a discussion on and off this list earlier this
week, several people confirmed that they had solved many problems
following this posting guide. It may not be as good as Polya's famous
"How to Solve It", but it's pretty good.)
hope this helps.
spencer
Pekka Vimpari wrote:
>Suppose I know the value of cumulative bivariate standard normal
distribution. How can I solve correlation between variables?
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>Pekka
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