Density of some (hyper-)spherical distributions.
dvmf(y, mu, k, logden = FALSE )
iagd(y, mu, logden = FALSE)
dpurka(y, theta, a, logden = FALSE)
dspcauchy(y, mu, rho, logden = FALSE)
dpkbd(y, mu, rho, logden = FALSE)A vector with the (log) density values of y.
A matrix or a vector with the data expressed in Euclidean coordinates, i.e. unit vectors.
The mean direction (unit vector) of the von Mises-Fisher, the IAG, the spherical Cauchy distribution, or of the Poisson kernel-based distribution.
The mean direction (unit vector) of the Purkayastha distribution.
The concentration parameter of the von Mises-Fisher distribution.
The concentration parameter of the Purkayastha distribution.
The \(\rho\) parameter of the spherical Cauchy distribution, or of the Poisson kernel-based distribution.
If you the logarithm of the density values set this to TRUE.
Michail Tsagris and Zehao Yu.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Zehao Yu zehaoy@email.sc.edu.
The density of the von Mises-Fisher, of the IAG, of the Purkayastha, of the spherical Cauchy distribution, or of the Poisson kernel-based distribution is computed.
Mardia K. V. and Jupp P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.
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.
Kato S. and McCullagh P. (2020). Some properties of a Cauchy family on the sphere derived from the Mobius transformations. Bernoulli, 26(4): 3224--3248. https://arxiv.org/pdf/1510.07679.pdf
Golzy M. and 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.
Sablica L., Hornik K. and Leydold J. (2023). Efficient sampling from the PKBD distribution. Electronic Journal of Statistics, 17(2): 2180--2209.
Zehao Yu and Xianzheng Huang (2024). A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension. Electronic Journal of Statististics, 18(1): 301--334.
Tsagris M., Papastamoulis P. and Kato S. (2024). Directional data analysis using the spherical Cauchy and the Poisson kernel-based distribution. https://arxiv.org/pdf/2409.03292.
kent.mle, rkent, esag.mle
m <- colMeans( as.matrix( iris[,1:3] ) )
y <- rvmf(1000, m = m, k = 10)
dvmf(y, k=10, m)
Run the code above in your browser using DataLab