VGAM (version 0.7-10)

normal1: Univariate normal distribution

Description

Maximum likelihood estimation of the two parameters of a univariate normal distribution.

Usage

normal1(lmean="identity", lsd="loge", emean=list(), esd=list(), zero=NULL)

Arguments

lmean

Link function applied to the mean. See Links for more choices.

lsd

Parameter link function applied to the standard deviation. See Links for more choices. Being a positive quantity, a log link is the default.

emean, esd

List. Extra argument for the links. See earg in Links for general information.

zero

An integer vector, containing the value 1 or 2. If so, the mean or standard deviation respectively are modelled as an intercept only. Usually, setting zero=2 will be used, if used at all. The default value NULL means both l

Value

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

Details

By default, the mean is the first linear/additive predictor and the log of the standard deviation is the second linear/additive predictor. The Fisher information matrix is diagonal.

References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

See Also

gaussianff, posnormal1, mix2normal1, tobit, cnormal1, fnormal1, skewnormal1, dcnormal1, studentt, dnorm.

Examples

ndata = data.frame(x = rnorm(nn <- 200))
ndata = transform(ndata, y = rnorm(nn, mean=1-3*x, sd=exp(1+0.2*x)))
fit = vglm(y ~ x, normal1, ndata, trace=TRUE)
coef(fit, matrix=TRUE)

# Generate a random sample from a N(mu=theta, sigma=theta)
# distribution with theta=10. Then estimate theta.
theta = 10
ndata = data.frame(y = rnorm(100, m=theta, sd=theta))
fit = vglm(y ~ 1, normal1(lsd="identity"), ndata,
           constraints = list("(Intercept)"=rbind(1,1)))
coef(fit, matrix=TRUE)