[R] Bivariate normal distribution and correlation

[Spencer Graves]

      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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