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

<

[hidden email]> 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(๐)=max{0,๐} distributions i.e max{0,๐1} + max{0,๐2} 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]]

>

> ______________________________________________

>

[hidden email] 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.

______________________________________________

[hidden email] mailing list -- To UNSUBSCRIBE and more, see

https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.