# [R] Bivariate ReLU Distribution

Abby Spurdle @purd|e@@ @end|ng |rom gm@||@com
Sat Jul 11 03:37:35 CEST 2020

```Last line should use outside = c (0, 1).
But not that important.

On Sat, Jul 11, 2020 at 1:31 PM Abby Spurdle <spurdle.a using gmail.com> wrote:
>
> NOTE: LIMITED TESTING
> (You may want to check this carefully, if you're interested in using it).
>
> library (kubik)
> library (mvtnorm)
>
> sim.cdf <- function (mx, my, sdx, sdy, cor, ..., n=2e5)
>     sim.cdf.2 (mx, my, sdx^2, sdy^2, sdx * sdy * cor, n=n)
>
> sim.cdf.2 <- function (mx, my, vx, vy, cov, ..., n=2e5)
> {   m <- c (mx, my)
>     v <- matrix (c (vx, cov, cov, vy), 2, 2)
>     u <- rmvnorm (2 * n, m, v)
>     for (i in 1:(2 * n) )
>         u [i] <- max (0, u [i])
>     z <- u [1:n] + u [(n + 1):(2 * n)]
>
>     P0 <- sum (z == 0) / n
>
>     z2 <- z [z != 0]
>     z2 <- c (-z2, z2)
>     de <- density (z2)
>     xFh <- chs.integral (de\$x, de\$y)
>
>     cx <- seq (0, max (de\$x), length.out=60)
>     cy <- xFh (cx)
>     cy <- cy - cy 
>     cy <- P0 + cy * (1 - P0) / cy 
>
>     cs = chs.constraints (increasing=TRUE)
>     chs (cx, cy, constraints=cs, outside = c (0, cy ) )
> }
>
> #X1, X2 means: 0 and 2
> #X1, Y2 sds: 1.5 and 3.5
> #cor (X1, X2): 0.75
> Fh <- sim.cdf (0, 2, 1.5, 3.5, 0.75)
>
> plot (Fh, ylim = c (0, 1.05), yaxs="i")
>
> #prob 1 < U < 2
> Fh (2) - Fh (1)
>
>
> On Sat, Jul 11, 2020 at 1:49 AM Arun Kumar Saha via R-help
> <r-help using r-project.org> wrote:
> >
> > Hi,
> > I would rather have a Statistics related question hope experts here can provide some suggestions. I have posted this request in some other forum but failed to generate meaningful response
> > I am looking for some technical document on deriving the Distribution function for sum of 2 ReLU(𝑋)=max{0,𝑋} distributions i.e max{0,𝑋1} + max{0,𝑋2} where X1 and X2 jointly follow some bivariate Nomal distribution.
> > There are few technical notes available for univariate ReLU distribution, however I failed to find any spec for bivariate/multivariate setup.
> > Any pointer on above subject will be highly helpful.
> >         [[alternative HTML version deleted]]
> >
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