[R] [FORGED] Re: correlated binomial random variables

[li li]

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.turner at 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
>