cardioid: Cardioid Distribution Family Function

View source: R/family.circular.R

cardioidR Documentation

Cardioid Distribution Family Function


Estimates the two parameters of the cardioid distribution by maximum likelihood estimation.


cardioid(lmu = extlogitlink(min = 0, max = 2*pi),
         lrho = extlogitlink(min = -0.5, max = 0.5),
         imu = NULL, irho = 0.3, nsimEIM = 100, zero = NULL)


lmu, lrho

Parameter link functions applied to the \mu and \rho parameters, respectively. See Links for more choices.

imu, irho

Initial values. A NULL means an initial value is chosen internally. See CommonVGAMffArguments for more information.

nsimEIM, zero

See CommonVGAMffArguments for more information.


The two-parameter cardioid distribution has a density that can be written as

f(y;\mu,\rho) = \frac{1}{2\pi} \left(1 + 2\, \rho \cos(y - \mu) \right)

where 0 < y < 2\pi, 0 < \mu < 2\pi, and -0.5 < \rho < 0.5 is the concentration parameter. The default link functions enforce the range constraints of the parameters.

For positive \rho the distribution is unimodal and symmetric about \mu. The mean of Y (which make up the fitted values) is \pi + (\rho/\pi) ((2 \pi-\mu) \sin(2 \pi-\mu) + \cos(2 \pi-\mu) - \mu \sin(\mu) - \cos(\mu)).


An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, rrvglm and vgam.


Numerically, this distribution can be difficult to fit because of a log-likelihood having multiple maximums. The user is therefore encouraged to try different starting values, i.e., make use of imu and irho.


Fisher scoring using simulation is used.


T. W. Yee


Jammalamadaka, S. R. and SenGupta, A. (2001). Topics in Circular Statistics, Singapore: World Scientific.

See Also

rcard, extlogitlink, vonmises.

CircStats and circular currently have a lot more R functions for circular data than the VGAM package.


## Not run: 
cdata <- data.frame(y = rcard(n = 1000, mu = 4, rho = 0.45))
fit <- vglm(y ~ 1, cardioid, data = cdata, trace = TRUE)
coef(fit, matrix=TRUE)
c(with(cdata, mean(y)), head(fitted(fit), 1))

## End(Not run)

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.