Thanks Dennis and Rolf. Yes. Simulation is one way. I think correlation does not determine the joint distribution so it will not be unique. Under specific settings, the joint probability of X, Y can be calculated. For example, let X=X_0+X_1 and Y=X_0+X_2, with X_0 being Binomial(n_0, p) and X_1, and X_2 are both Binomial(n, p). X_0, X_1, and X_2 are all independent. Then X, Y are correlated and P(X <= t, Y <= t) can be exactly calculated.
Thanks! Hanna 2015-10-05 18:00 GMT-04:00, Rolf Turner <r.tur...@auckland.ac.nz>: > On 06/10/15 04:43, li li wrote: >> Hi all, >> Using the "bindata" package, it is possible to gerenerate >> correlated binomial random variables both with the same number of >> trials, say n. I am wondering whether there is an R function to >> calculate the joint probability distribution of the correlated >> binomial random variables. Say if X is binomial (n, p1) and Y is >> binomial (n, p2) and the correlation between X and Y is rho and we >> want to calculate >> P(X <= c, Y <= c). > > (1) The use of correlation in the context of binary or binomial variates > makes little or no sense, it seems to me. Correlation is basically > useful for quantifying linear relationships between continuous variates. > Linear relationships between count variates are of at best limited > interest. > > (2) I suspect that the correlation does not determine a unique joint > distribution of X and Y. If my suspicion is correct then there is not a > unique (well-defined) answer to the question "What is > Pr(X <= x, Y <= y)?" > > cheers, > > Rolf Turner > > -- > Technical Editor ANZJS > Department of Statistics > University of Auckland > Phone: +64-9-373-7599 ext. 88276 > ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
