genrayleigh: Generalized Rayleigh Distribution Family Function

View source: R/family.others.R

genrayleighR Documentation

Generalized Rayleigh Distribution Family Function


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


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


lscale, lshape

Link function for the two positive parameters, scale and shape. See Links for more choices.

iscale, ishape

Numeric. Optional initial values for the scale and shape parameters.

nsimEIM, zero

See CommonVGAMffArguments.


Numeric and positive. Tolerance for testing whether the second shape parameter is either 1 or 2. If so then the working weights need to handle these singularities.


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.


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


We define scale as the reciprocal of the scale parameter used by Kundu and Raqab (2005).


J. G. Lauder and T. W. Yee


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.


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)

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