Generalized Rayleigh Distribution Family Function

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)

Arguments

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.

tol12

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.

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.

Value

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

References

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

Author

J. G. Lauder and T. W. Yee

Note

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

Examples

if (FALSE) Scale <- exp(1); shape <- exp(1)
rdata <- data.frame(y = rgenray(n = 1000, scale = Scale, shape = shape))
#> Error: object 'Scale' not found
fit <- vglm(y ~ 1, genrayleigh, data = rdata, trace = TRUE)
#> Error in eval(mf, parent.frame()): object 'rdata' not found
c(with(rdata, mean(y)), head(fitted(fit), 1))
#> Error: object 'rdata' not found
coef(fit, matrix = TRUE)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'coef': object 'fit' not found
Coef(fit)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'Coef': object 'fit' not found
summary(fit)  # \dontrun{}
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'fit' not found