normal1 {VGAM}R Documentation

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 linear/additive predictors are modelled as functions of the explanatory variables.

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.

Value

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

Note

The response should be univariate. Multivariate responses are more generally handled using gaussianff, however this only handles the mean and the variance-covariance matrices are assumed known.

Author(s)

T. W. Yee

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

n = 200
x = rnorm(n)
y = rnorm(n, mean=1-3*x, sd=exp(1+0.2*x))
fit = vglm(y ~ x, normal1)
coef(fit, matrix=TRUE)

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

[Package VGAM version 0.7-7 Index]