Binorm {VGAM} | R Documentation |
Bivariate Normal Distribution Cumulative Distribution Function
Description
Density, cumulative distribution function and random generation for the bivariate normal distribution distribution.
Usage
dbinorm(x1, x2, mean1 = 0, mean2 = 0, var1 = 1, var2 = 1, cov12 = 0,
log = FALSE)
pbinorm(q1, q2, mean1 = 0, mean2 = 0, var1 = 1, var2 = 1, cov12 = 0)
rbinorm(n, mean1 = 0, mean2 = 0, var1 = 1, var2 = 1, cov12 = 0)
pnorm2(x1, x2, mean1 = 0, mean2 = 0, var1 = 1, var2 = 1, cov12 = 0)
Arguments
x1 , x2 , q1 , q2 |
vector of quantiles. |
mean1 , mean2 , var1 , var2 , cov12 |
vector of means, variances and the covariance. |
n |
number of observations.
Same as |
log |
Logical.
If |
Details
The default arguments correspond to the standard bivariate normal
distribution with correlation parameter .
That is, two independent standard normal distributions.
Let
sd1
(say) be sqrt(var1)
and
written , etc.
Then the general formula for the correlation coefficient is
where
is argument
cov12
.
Thus if arguments var1
and var2
are left alone then
cov12
can be inputted with .
One can think of this function as an extension of
pnorm
to two dimensions, however note
that the argument names have been changed for VGAM
0.9-1 onwards.
Value
dbinorm
gives the density,
pbinorm
gives the cumulative distribution function,
rbinorm
generates random deviates ( by 2 matrix).
Warning
Being based on an approximation, the results of pbinorm()
may be negative!
Also,
pnorm2()
should be withdrawn soon;
use pbinorm()
instead because it is identical.
Note
For rbinorm()
,
if the th variance-covariance matrix is not
positive-definite then the
th row is all
NA
s.
References
pbinorm()
is
based on Donnelly (1973),
the code was translated from FORTRAN to ratfor using struct, and
then from ratfor to C manually.
The function was originally called bivnor
, and TWY only
wrote a wrapper function.
Donnelly, T. G. (1973). Algorithm 462: Bivariate Normal Distribution. Communications of the ACM, 16, 638.
See Also
Examples
yvec <- c(-5, -1.96, 0, 1.96, 5)
ymat <- expand.grid(yvec, yvec)
cbind(ymat, pbinorm(ymat[, 1], ymat[, 2]))
## Not run: rhovec <- seq(-0.95, 0.95, by = 0.01)
plot(rhovec, pbinorm(0, 0, cov12 = rhovec),
xlab = expression(rho), lwd = 2,
type = "l", col = "blue", las = 1)
abline(v = 0, h = 0.25, col = "gray", lty = "dashed")
## End(Not run)