VGAM (version 1.1-14)

genrayleigh: Generalized Rayleigh Distribution Family Function

Description

Estimates the two parameters of the generalized Rayleigh distribution by maximum likelihood estimation.

Usage

genrayleigh(lscale = "loglink", lshape = "loglink",
            iscale = NULL,   ishape = NULL,
            tol12 = 1e-05, nsimEIM = 300, zero = 2)

Value

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

and vgam.

Details

The generalized Rayleigh distribution has density function $$f(y;b = scale,s = shape) = (2 s y/b^{2}) e^{-(y/b)^{2}} (1 - e^{-(y/b)^{2}})^{s-1}$$ where \(y > 0\) and the two parameters, \(b\) and \(s\), are positive. The mean cannot be expressed nicely so the median is returned as the fitted values. Applications of the generalized Rayleigh distribution include modeling strength data and general lifetime data. Simulated Fisher scoring is implemented.

References

Kundu, D., Raqab, M. C. (2005). Generalized Rayleigh distribution: different methods of estimations. Computational Statistics and Data Analysis, 49, 187--200.

See Also

dgenray, rayleigh.

Examples

if (FALSE) Scale <- exp(1); shape <- exp(1)
rdata <- data.frame(y = rgenray(n = 1000, scale = Scale, shape = shape))
fit <- vglm(y ~ 1, genrayleigh, data = rdata, trace = TRUE)
c(with(rdata, mean(y)), head(fitted(fit), 1))
coef(fit, matrix = TRUE)
Coef(fit)
summary(fit)