maxwell: Maxwell Regression Family Function

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/family.univariate.R

Description

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

Usage

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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

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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)

Example output

Loading required package: stats4
Loading required package: splines
VGLM    linear loop  1 :  coefficients = 2.2306871
VGLM    linear loop  2 :  coefficients = 1.9831625
VGLM    linear loop  3 :  coefficients = 2.0091814
VGLM    linear loop  4 :  coefficients = 2.0095258
VGLM    linear loop  5 :  coefficients = 2.0095258
            loge(rate)
(Intercept)   2.009526
    rate 
7.459779 

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.