# genrayleigh: Generalized Rayleigh Distribution Family Function In VGAM: Vector Generalized Linear and Additive Models

 genrayleigh R Documentation

## 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)
``````

### 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`.

### Note

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

### Author(s)

J. G. Lauder and T. W. Yee

### References

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

`dgenray`, `rayleigh`.

### Examples

``````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)