Density of some (hyper-)spherical distributions
Density of some (hyper-)spherical distributions.
dvmf(y, k, mu, logden = FALSE ) iagd(y, mu, logden = FALSE) dpurka(y, a, theta, logden = FALSE)
y |
A matrix or a vector with the data expressed in Euclidean coordinates, i.e. unit vectors. |
k |
The concentration parameter of the von Mises-Fisher distribution. |
a |
The concentration parameter of the Purkayastha distribution. |
mu |
The mean direction (unit vector) of the von Mises-Fisher distribution or the mean direction of the IAG distribution. |
theta |
The median direction for the Purkayastha distribution. |
logden |
If you the logarithm of the density values set this to TRUE. |
The density of the von Mises-Fisher, of the IAG or of the Purkayastha distribution is computed.
A vector with the (log) density values of y.
Michail Tsagris
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr
Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.
Kent John (1982). The Fisher-Bingham distribution on the sphere. Journal of the Royal Statistical Society, Series B, 44(1): 71-80.
Purkayastha S. (1991). A Rotationally Symmetric Directional Distribution: Obtained through Maximum Likelihood Characterization. The Indian Journal of Statistics, Series A, 53(1): 70-83
Cabrera J. and Watson G. S. (1990). On a spherical median related distribution. Communications in Statistics-Theory and Methods, 19(6): 1973-1986.
m <- colMeans( as.matrix( iris[,1:3] ) ) y <- rvmf(1000, m = m, k = 10) dvmf(y, k=10, m )
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