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Directional (version 6.8)

Cumulative distribution function of circular distributions: Cumulative distribution function of circular distributions

Description

Cumulative probability distribution of circular distributions.

Usage

pvm(u, m, k, rads = FALSE)
pspml(u, mu, rads = FALSE)
pwrapcauchy(u, m, rho, rads = FALSE)
pcircpurka(u, m, a, rads = FALSE)
pcircbeta(u, m, a, b, rads = FALSE)
pcardio(u, m, rho, rads = FALSE)
pcircexp(u, lambda, rads = FALSE)
pcipc(u, omega, g, rads = FALSE)
pgcpc(u, omega, g, rho, rads = FALSE)
pmmvm(u, m, k, N, rads = FALSE)

Value

The probability that of u being less than \(\theta\), where u follows a circular distribution.

Arguments

u

A numerical value, either in radians or in degrees.

m

The mean direction of the von Mises and the multi-modal von Mises distribution in radians or in degrees.

mu

The mean vector, a vector with two values for the "pspml".

omega

The location parameter of the CIPC and GCPC distributions.

g

The norm of the mean vector for the CIPC and GCPC distributions.

k

The concentration parameter, \(\kappa\).

lambda

The \(\lambda\) parameter of the circular exponential distribution. This must be positive.

a

The \(\alpha\) parameter of the circular Purkayastha distribution or the \(\alpha\) parameter of the circular Beta distribution.

b

The \(\beta\) parameter of the circular beta distribution.

rho

The \(\rho\) parameter of the Cardioid, wrapped Cauchy and GCPC distributions.

N

The number of modes to consider in the multi-modal von Mises distribution.

rads

If the data are in radians, this should be TRUE and FALSE otherwise.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

Details

This value calculates the probability of u being less than some value \(\theta\).

References

Arthur Pewsey, Markus Neuhauser, and Graeme D. Ruxton (2013). Circular Statistics in R.

Barnett M. J. and Kingston R. L. (2024). A note on the Hendrickson-Lattman phase probability distribution and its equivalence to the generalized von Mises distribution. Journal of Applied Crystallography, 57(2).

Jammalamadaka S. R. and Kozubowski T. J. (2003). A new family of circular models: The wrapped Laplace distributions. Advances and Applications in Statistics, 3(1): 77--103.

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.

Paula F. V., Nascimento A. D., Amaral G. J. and Cordeiro G. M. (2021). Generalized Cardioid distributions for circular data analysis. Stats, 4(3): 634--649.

Zheng Sun (2009). Comparing measures of fit for circular distributions. MSc Thesis, University of Victoria. file:///C:/Users/mtsag/Downloads/zhengsun_master_thesis.pdf

See Also

group.gof, dvm, dcircexp, purka.mle, dcircpurka, dmmvm

Examples

Run this code
pvm(1, 2, 10, rads = TRUE)
pmmvm(1, 2, 10, 3, rads = TRUE)
pcircexp(c(1, 2), 2, rads = TRUE)
pcircpurka(2, 3, 0.3)

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