Cumulative distribution function of circular distributions {Directional}

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)

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.

Details

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

Value

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

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

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

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)