VGAM (version 1.1-6)

# maxwell: 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

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.

## Value

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

## 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 $$(3\pi - 8)/(\pi a)$$.

## References

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

Maxwell, rayleigh, poisson.points.

## Examples

Run this code
# NOT RUN {
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)
# }


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