# [R] Bivariate normal

Sasha Pustota popgen at gmail.com
Wed Oct 1 20:28:21 CEST 2008

P.S. just "pnorm(x, mean=m, sd=s)", not  "1-pnorm(x, mean=m, sd=s) +
pnorm(-x, mean=m, sd=s)"

On Wed, Oct 1, 2008 at 2:04 PM, Sasha Pustota <popgen at gmail.com> wrote:
> Thanks Jay. I realized that I was doing it a silly way shortly after I
> posted and that the answer i was looking for is simply
>
> condXY(y, x, my, mx, r) * dnorm(y, my)
>
> condXY <- function(y, x, my, mx, r) {
>  m <- mx + r*(y - my)
>  s <- sqrt(1-r^2)
>  p <- 1 - pnorm(x, mean=m, sd=s) + pnorm(-x, mean=m, sd=s)
> }
>
>
> On Wed, Oct 1, 2008 at 1:11 PM, G. Jay Kerns <gkerns at ysu.edu> wrote:
>> Dear Sasha,
>>
>> On Wed, Oct 1, 2008 at 11:43 AM, Sasha Pustota <popgen at gmail.com> wrote:
>>> Package mvtnorm provides dmvnorm, pmvnorm that can be used to compute
>>> Pr(X=x,Y=y) and Pr(X<x,Y<y) for a bivariate normal.
>>>
>>> Are there functions that would compute Pr(X<x,Y=y)?
>>> I'm currently using "integrate" with dmvnorm but it is too slow.
>>
>>
>> Strictly speaking, the probability that you are asking to calculate is
>> always 0, for every value of y.  The reason is that the quantity you
>> are requesting is the _volume_ of a vertical slice, at the value y,
>> which is zero.  It may be useful to think carefully about the problem
>> you are trying to solve...  perhaps a conditional probability is more
>> appropriate.
>>
>> You did not say exactly which integral you are trying to compute:
>> conceivably it would be
>>
>> \int_{-\infty}^{x}  f(u, y) du,
>>
>> where f(.,.) is the bivariate normal pdf.  If this is indeed what you
>> want, then a work-around would be to calculate P( X < x | Y = y ).  We
>> know that given Y=y, X is normal with mean and variance formulas given
>> in most introductory statistics books.  Thus, you could compute P( X <
>> x | Y = y ) with pnorm(x, mean = something, sd = something).
>>
>> In that case, the integral above would simply be P( X < x | Y=y ) *
>> f(y), where f(y) is the marginal pdf of Y (a dnorm).
>>
>> Note that the above is assuming that y is a fixed constant;  if not,
>> then you may want to check out the Ryacas package.
>>
>> I hope that this helps,
>> Jay
>>
>>
>>
>>
>>
>> ***************************************************
>> G. Jay Kerns, Ph.D.
>> Associate Professor
>> Department of Mathematics & Statistics
>> Youngstown State University
>> Youngstown, OH 44555-0002 USA
>> Office: 1035 Cushwa Hall
>> Phone: (330) 941-3310 Office (voice mail)
>> -3302 Department
>> -3170 FAX
>> E-mail: gkerns at ysu.edu
>> http://www.cc.ysu.edu/~gjkerns/
>>
>