rwnorm {BAMBI} | R Documentation |
The univariate Wrapped Normal distribution
Description
The univariate Wrapped Normal distribution
Usage
rwnorm(n = 1, kappa = 1, mu = 0)
dwnorm(x, kappa = 1, mu = 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. |
kappa |
vector of concentration (inverse-variance) parameters; |
mu |
vector of means. |
x |
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
If mu
and kappa
are not specified they assume the default values of 0
and 1
respectively.
The univariate wrapped normal distribution has density
f(x) = \sqrt(\kappa/(2\pi)) \sum \exp(-\kappa/2 (x - \mu(2\pi\omega))^2)
where the sum extends over all integers \omega
,
and is approximated by a sum over \omega
in \{-M, -M+1, ..., M-1, M \}
if int.displ =
M
.
Value
dwnorm
gives the density and rwnorm
generates random deviates.
Examples
kappa <- 1:3
mu <- 0:2
x <- 1:10
n <- 10
# when x and both parameters are scalars, dwnorm returns a single density
dwnorm(x[1], kappa[1], mu[1])
# when x is a vector but both the parameters are scalars, dmv returns a vector of
# densities calculated at each entry of x with the same parameters
dwnorm(x, kappa[1], mu[1])
# if x is scalar and at least one of the two paraemters is a vector, both parameters are
# recycled to the same length, and dwnorm returns a vector of with ith element being the
# density evaluated at x with parameter values kappa[i] and mu[i]
dwnorm(x[1], kappa, mu)
# if x and at least one of the two paraemters is a vector, x and the two parameters are
# recycled to the same length, and dwnorm returns a vector of with ith element being the
# density at ith element of the (recycled) x with parameter values kappa[i] and mu[i]
dwnorm(x, kappa, mu)
# when parameters are all scalars, number of observations generated by rwnorm is n
rwnorm(n, kappa[1], mu[1])
# when at least one of the two parameters is a vector, both are recycled to the same length,
# n is ignored, and the number of observations generated by rwnorm is the same as the length
# of the recycled vectors
rwnorm(n, kappa, mu)