Simulation of random values from some circular distributions.
rvonmises(n, m, k, rads = TRUE)
rwrapcauchy(n, m, rho, rads = TRUE)
rspml(n, mu, rads = TRUE)
rcircbeta(n, m, a, b, rads = TRUE)
rcircpurka(n, m, a, rads = TRUE)
rcircexp(n, lambda, rads = TRUE)A vector with the simulated data.
The sample size.
The mean angle expressed in radians or degrees.
The mean vector of the SPML in \(R^2\).
The concentration parameter of the von Mises distribution. If k is zero the sample will be generated from the uniform distribution over \((0, 2\pi)\).
The \(\rho\) parameter of the Wrapped Cauchy distribution.
The \(\alpha\) parameter of the beta distribution.
The \(\beta\) parameter of the beta distribution.
The \(\lambda\) parameter of the circular (wrapped) exponential distribution.
If the mean angle is expressed in radians, this should be TRUE and FALSE otherwise. The simulated data will be expressed in radians or degrees depending on what the mean angle is expressed.
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.
For the von Mises distribution, the mean direction is transformed to the Euclidean coordinates (i.e. unit vector) and then the rvmf function is employed. It uses a rejection smapling as suggested by Andrew Wood in 1994. I have mentioned the description of the algorithm as I found it in Dhillon and Sra in 2003. Finally, the data are transformed to radians or degrees.
For the wrapped Cauchy and wrapped exponential distributions the function generates Cauchy or exponential values \(x\) and then wrapps them around the circle \(x = x(mod 2 \pi)\). For the circular beta the function has some extra steps (see Zheng Sun's master thesis).
Wood, A. T. (1994). Simulation of the von Mises Fisher distribution. Communications in statistics-simulation and computation, 23(1): 157-164.
Dhillon, I. S., & Sra, S. (2003). Modeling data using directional distributions. Technical Report TR-03-06, Department of Computer Sciences, The University of Texas at Austin. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.75.4122&rep=rep1&type=pdf
Zheng Sun (2006). Comparing measures of fit for circular distributions. Master thesis, University of Victoria. https://dspace.library.uvic.ca/bitstream/handle/1828/2698/zhengsun_master_thesis.pdf;sequence=1
Lai, M. (1994). Some results in the statistical analysis of directional data. Master thesis, University of Hong Kong.
Presnell Brett, Morrison Scott P. and Littell Ramon C. (1998). Projected multivariate linear models for directional data. Journal of the American Statistical Association, 93(443): 1068-1077.
Purkayastha S. (1991). A Rotationally Symmetric Directional Distribution: Obtained through Maximum Likelihood Characterization. The Indian Journal of Statistics, Series A, 53(1): 70-83
Jammalamadaka, S. R. & Kozubowski, T. J. (2003). A new family of circular models: The wrapped Laplace distributions. Advances and Applications in Statistics, 3(1), 77-103.
circ.summary, rvmf, racg
x <- rvonmises(100, 2, 25, rads = TRUE)
circ.summary(x, rads = TRUE)
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