VGAM (version 1.1-9)

felix: Felix Distribution Family Function

Description

Estimates the parameter of a Felix distribution by maximum likelihood estimation.

Usage

felix(lrate = extlogitlink(min = 0, max = 0.5), imethod = 1)

Value

An object of class "vglmff"

(see vglmff-class). The object is used by modelling functions such as vglm

and vgam.

Arguments

lrate

Link function for the parameter, called \(a\) below; see Links for more choices and for general information.

imethod

See CommonVGAMffArguments. Valid values are 1, 2, 3 or 4.

Author

T. W. Yee

Details

The Felix distribution is an important basic Lagrangian distribution. The density function is $$f(y;a) = \frac{ 1 }{((y-1)/2)!} y^{(y-3)/2} a^{(y-1)/2} \exp(-ay) $$ where \(y=1,3,5,\ldots\) and \(0 < a < 0.5\). The mean is \(1/(1-2a)\) (returned as the fitted values). Fisher scoring is implemented.

References

Consul, P. C. and Famoye, F. (2006). Lagrangian Probability Distributions, Boston, USA: Birkhauser.

See Also

dfelix, borel.tanner.

Examples

fdata <- data.frame(y = 2 * rpois(n = 200, 1) + 1)  # Not real data!
fit <- vglm(y ~ 1, felix, data = fdata, trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)
Coef(fit)
summary(fit)