normal1 {VGAM} | R Documentation |
Maximum likelihood estimation of the two parameters of a univariate normal distribution.
normal1(lmean="identity", lsd="loge", emean=list(), esd=list(), zero=NULL)
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.
|
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.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
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.
T. W. Yee
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.
gaussianff
,
posnormal1
,
mix2normal1
,
tobit
,
cnormal1
,
fnormal1
,
skewnormal1
,
dcnormal1
,
studentt
,
dnorm
.
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)