maxwell {VGAM} | R Documentation

## Maxwell Distribution Family Function

### Description

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

### Usage

    maxwell(link = "loge", earg=list())

### Arguments

`link` | Parameter link function applied to the parameter a. See `Links` for more choices. A log link is the default because the parameter is positive.
`earg` | List. Extra argument for the link. See `earg` in `Links` for general information.

### Details

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

f(y) = 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

A related distribution is the Rayleigh distribution. Fisher-scoring and Newton-Raphson are the same here.

### Author(s)

T. W. Yee

### References

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

### See Also

`Maxwell`, `rayleigh`.

### Examples

    y = rmaxwell(n <- 1000, a=exp(2))
    fit = vglm(y ~ 1, maxwell, trace=TRUE, crit="c")
    coef(fit, matrix=TRUE)
    Coef(fit)

[Package VGAM version 0.7-9 Index]