rwnorm2mix {BAMBI} | R Documentation |
The bivariate Wrapped Normal mixtures
Description
The bivariate Wrapped Normal mixtures
Usage
rwnorm2mix(n, kappa1, kappa2, kappa3, mu1, mu2, pmix, ...)
dwnorm2mix(x, kappa1, kappa2, kappa3, mu1, mu2, pmix, int.displ, log = FALSE)
Arguments
n |
number of observations. |
kappa1 , kappa2 , kappa3 |
vectors of concentration parameters; |
mu1 , mu2 |
vectors of mean parameters. |
pmix |
vector of mixture proportions. |
... |
additional arguments passed to rmvnorm from package |
x |
matrix of angles (in radians) where the density is to be evaluated, with each row being a single bivariate vector of angles. |
int.displ |
integer displacement. If |
log |
logical. Should the log density be returned instead? |
Details
All the argument vectors pmix, kappa1, kappa2, kappa3, mu1
and mu2
must be of the same length,
with j
-th element corresponding to the j
-th component of the mixture distribution.
The bivariate wrapped normal mixture distribution with component size K = length(pmix)
has density
g(x) = \sum p[j] * f(x; \kappa_1[j], \kappa_2[j], \kappa_3[j], \mu_1[j], \mu_2[j])
where the sum extends over j
; p[j]; \kappa_1[j], \kappa_2[j], \kappa_3[j]
; and \mu_1[j], \mu_2[j]
respectively denote the mixing proportion,
the three concentration parameters and the two mean parameter for the j
-th component, j = 1, ..., K
,
and f(. ; \kappa_1, \kappa_2, \kappa_3, \mu_1, \mu_2)
denotes the density function of the wrapped normal distribution
with concentration parameters \kappa_1, \kappa_2, \kappa_3
and mean parameters \mu_1, \mu_2
.
Value
dwnorm2mix
computes the density and rwnorm2mix
generates random deviates from the mixture density.
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)
pmix <- c(0.3, 0.4, 0.3)
x <- diag(2, 2)
n <- 10
# mixture densities calculated at the rows of x
dwnorm2mix(x, kappa1, kappa2, kappa3, mu1, mu2, pmix)
# number of observations generated from the mixture distribution is n
rwnorm2mix(n, kappa1, kappa2, kappa3, mu1, mu2, pmix)