Trivariate Normal Distribution Density and Random Variates
Density and random generation for the trivariate normal distribution distribution.
dtrinorm(x1, x2, x3, mean1 = 0, mean2 = 0, mean3 = 0,
var1 = 1, var2 = 1, var3 = 1,
cov12 = 0, cov23 = 0, cov13 = 0, log = FALSE)
rtrinorm(n, mean1 = 0, mean2 = 0, mean3 = 0,
var1 = 1, var2 = 1, var3 = 1,
cov12 = 0, cov23 = 0, cov13 = 0)x1, x2, x3 |
vector of quantiles. |
mean1, mean2, mean3 |
vectors of means. |
var1, var2, var3 |
vectors of variances. |
cov12, cov23, cov13 |
vectors of covariances. |
n |
number of observations.
Same as |
log |
Logical.
If |
The default arguments correspond to the standard trivariate normal
distribution with correlation parameters equal to 0,
which corresponds to three independent standard normal distributions.
Let sd1 (say) be sqrt(var1) and
written sigma_1, etc.
Then the general formula for each correlation coefficient is
of the form
rho12 = cov12 /
(sigma_1 * sigma_2),
and similarly for the two others.
Thus if the var arguments are left alone then
the cov can be inputted with rhos.
dtrinorm gives the density,
rtrinorm generates random deviates (n by 3 matrix).
dtrinorm()'s arguments might change in the future!
It's safest to use the full argument names
to future-proof possible changes!
For rtrinorm(),
if the ith variance-covariance matrix is not
positive-definite then the ith row is all NAs.
## Not run: nn <- 1000
tdata <- data.frame(x2 = sort(runif(nn)))
tdata <- transform(tdata, mean1 = 1 + 2 * x2,
mean2 = 3 + 1 * x2, mean3 = 4,
var1 = exp( 1), var2 = exp( 1), var3 = exp( 1),
rho12 = rhobit( 1, inverse = TRUE),
rho23 = rhobit( 1, inverse = TRUE),
rho13 = rhobit(-1, inverse = TRUE))
ymat <- with(tdata, rtrinorm(nn, mean1, mean2, mean3,
var1, var2, var3,
sqrt(var1)*sqrt(var1)*rho12,
sqrt(var2)*sqrt(var3)*rho23,
sqrt(var1)*sqrt(var3)*rho13))
pairs(ymat, col = "blue")
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