VGAM (version 0.9-0)

maxwell: Maxwell Distribution Family Function

Description

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

Usage

maxwell(link = "loge", zero = NULL)

Arguments

link, zero

Parameter link function applied to $a$. See Links for more choices and information; a log link is the default because the parameter is positive. More information is at

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.: CRC Press.

See Also

Maxwell, rayleigh.

Examples

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