R: Maxwell Regression Family Function

maxwell {VGAM} | R Documentation

## Maxwell Regression Family Function

### Description

Estimating the parameter of the Maxwell distribution by maximum likelihood estimation.

### Usage

    maxwell(link = "loglink", zero = NULL, parallel = FALSE,
            type.fitted = c("mean", "percentiles", "Qlink"),
            percentiles = 50)

### Arguments

`link` | Parameter link function applied to a, which is called the parameter `rate`. See `Links` for more choices and information; a log link is the default because the parameter is positive. More information is at `CommonVGAMffArguments`.
`zero, parallel` | See `CommonVGAMffArguments`.
`type.fitted, percentiles` | See `CommonVGAMffArguments` for information. Using `"Qlink"` is for quantile-links in VGAMextra.

### Details

The Maxwell distribution, which is used in the area of thermodynamics, has a probability density function that can be written

f(y;a) = sqrt(2/pi) * a^(3/2) * y^2 * exp(-0.5*a*y^2)

for y>0 and a>0. The mean of Y is sqrt(8 / (a * pi)) (returned as the fitted values), and its variance is (3*pi - 8)/(pi*a).

### Value

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

### Note

Fisher-scoring and Newton-Raphson are the same here. A related distribution is the Rayleigh distribution. This VGAM family function handles multiple responses. This VGAM family function can be mimicked by `poisson.points(ostatistic = 1.5, dimension = 2)`.

### Author(s)

T. W. Yee

### References

von Seggern, D. H. (1993). CRC Standard Curves and Surfaces, Boca Raton, FL, USA: CRC Press.

### See Also

`Maxwell`, `rayleigh`, `poisson.points`.

### Examples

    mdata <- data.frame(y = rmaxwell(1000, rate = exp(2)))
    fit <- vglm(y ~ 1, maxwell, data = mdata, trace = TRUE, crit = "coef")
    coef(fit, matrix = TRUE)
    Coef(fit)

[Package VGAM version 1.1-3 Index]