Density function and random number generation from the Poisson kernel-based
Distribution with mean direction vector mu
and concentration parameter
rho
.
Usage
dpkb(x, mu, rho, logdens = FALSE)
rpkb(
n,
mu,
rho,
method = "rejvmf",
tol.eps = .Machine$double.eps^0.25,
max.iter = 1000
)
Arguments
- x
Matrix (or data.frame) with number of columns >=2.
- mu
location vector parameter with length indicating the dimension of generated points.
- rho
is the concentration parameter, with 0 <= rho < 1.
- logdens
Logical; if 'TRUE', densities d are given as log(d).
- n
number of observations.
- method
string that indicates the method used for sampling observations. The available methods are
'rejvmf'
acceptance-rejection algorithm using von Mises-Fisher envelops (Algorithm in Table 2 of Golzy and Markatou 2020);'rejacg'
using angular central Gaussian envelops (Algorithm in Table 1 of Sablica et al. 2023);'rejpsaw'
using projected Saw distributions (Algorithm in Table 2 of Sablica et al. 2023).
- tol.eps
the desired accuracy of convergence tolerance (for 'rejacg' method).
- max.iter
the maximum number of iterations (for 'rejacg' method).
Value
dpkb
gives the density value.
rpkb
generates random observations from the PKBD.
The number of observations generated is determined by n
for
rpkb
. This function returns a list with the matrix of generated
observations x
, the number of tries numTries
and the number of
acceptances numAccepted
.
Details
If the chosen method is 'rejacg', the function uniroot
, from the
stat
package, is used to estimate the beta parameter. In this case,
the complete results are provided as output.
References
Golzy, M., Markatou, M. (2020) Poisson Kernel-Based Clustering on the Sphere: Convergence Properties, Identifiability, and a Method of Sampling, Journal of Computational and Graphical Statistics, 29:4, 758-770, DOI: 10.1080/10618600.2020.1740713.
Sablica L., Hornik K., Leydold J. (2023) "Efficient sampling from the PKBD distribution", Electronic Journal of Statistics, 17(2), 2180-2209.