Density of the spherical Kent and ESAG distributions
Density of the spherical Kent and ESAG distributions.
dkent(y, G, param, logden = FALSE ) desag(y, mu, gam, logden = FALSE)
y |
A matrix or a vector with the data expressed in Euclidean coordinates, i.e. unit vectors. |
G |
For the Kent distribution only, a 3 x 3 matrix whose first column is the mean direction. The second and third columns are the major and minor axes respectively. |
param |
For the Kent distribution a vector with the concentration κ and ovalness β parameters. The ψ has been absorbed inside the matrix G. |
mu |
The mean vector the ESAG distribution, a vector in R^3. |
gam |
The two gamma parameters of the ESAG distribution. |
logden |
If you the logarithm of the density values set this to TRUE. |
The density of the spherical Kent or spherical ESAG 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.
Paine P.J., Preston S.P., Tsagris M. and Wood A.T.A. (2018). An Elliptically Symmetric Angular Gaussian Distribution. Statistics and Computing, 28(3):689–697.
m <- colMeans( as.matrix( iris[,1:3] ) ) y <- rkent(1000, k = 10, m = m, b = 4) mod <- kent.mle(y) dkent( y, G = mod$G, param = mod$param )
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