[R] Bivariate ReLU Distribution

[Abby Spurdle]

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 [1]
    cy <- P0 + cy * (1 - P0) / cy [60]

    cs = chs.constraints (increasing=TRUE)
    chs (cx, cy, constraints=cs, outside = c (0, cy [60]) )
}

#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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