rwnorm2 {BAMBI} | R Documentation |
The bivariate Wrapped Normal distribution
Description
The bivariate Wrapped Normal distribution
Usage
rwnorm2(n, kappa1 = 1, kappa2 = 1, kappa3 = 0, mu1 = 0, mu2 = 0, ...)
dwnorm2(
x,
kappa1 = 1,
kappa2 = 1,
kappa3 = 0,
mu1 = 0,
mu2 = 0,
int.displ,
log = FALSE
)
Arguments
n |
number of observations. Ignored if at least one of the other parameters have length k > 1, in which case, all the parameters are recycled to length k to produce k random variates. |
kappa1 , kappa2 , kappa3 |
vectors of concentration parameters; |
mu1 , mu2 |
vectors of mean parameters. |
... |
additional arguments passed to rmvnorm from package |
x |
bivariate vector or a two-column matrix with each row being a bivariate vector of angles (in radians) where the densities are to be evaluated. |
int.displ |
integer displacement. If |
log |
logical. Should the log density be returned instead? |
Details
The bivariate wrapped normal density at the point is given by,
where
the sum extends over all pairs of integers ,
and is approximated by a sum over
in
if
int.displ =
.
Note that above density is essentially the "wrapped" version of a bivariate normal density with mean
and dispersion matrix , where
| | |
|
| | | |
| | .
|
Value
dwnorm2
gives the density and rwnorm2
generates random deviates.
Examples
kappa1 <- c(1, 2, 3)
kappa2 <- c(1, 6, 5)
kappa3 <- c(0, 1, 2)
mu1 <- c(1, 2, 5)
mu2 <- c(0, 1, 3)
x <- diag(2, 2)
n <- 10
# when x is a bivariate vector and parameters are all scalars,
# dwnorm2 returns single density
dwnorm2(x[1, ], kappa1[1], kappa2[1], kappa3[1], mu1[1], mu2[1])
# when x is a two column matrix and parameters are all scalars,
# dmvsin returns a vector of densities calculated at the rows of
# x with the same parameters
dwnorm2(x, kappa1[1], kappa2[1], kappa3[1], mu1[1], mu2[1])
# if x is a bivariate vector and at least one of the parameters is
# a vector, all parameters are recycled to the same length, and
# dwnorm2 returns a vector of with ith element being the density
# evaluated at x with parameter values kappa1[i], kappa2[i],
# kappa3[i], mu1[i] and mu2[i]
dwnorm2(x[1, ], kappa1, kappa2, kappa3, mu1, mu2)
# if x is a two column matrix and at least one of the parameters is
# a vector, rows of x and the parameters are recycled to the same
# length, and dwnorm2 returns a vector of with ith element being the
# density evaluated at ith row of x with parameter values kappa1[i],
# kappa2[i], # kappa3[i], mu1[i] and mu2[i]
dwnorm2(x, kappa1, kappa2, kappa3, mu1, mu2)
# when parameters are all scalars, number of observations generated
# by rwnorm2 is n
rwnorm2(n, kappa1[1], kappa2[1], kappa3[1], mu1[1], mu2[1])
# when at least one of the parameters is a vector, all parameters are
# recycled to the same length, n is ignored, and the number of
# observations generated by rwnorm2 is the same as the length of the
# recycled vectors
rwnorm2(n, kappa1, kappa2, kappa3, mu1, mu2)