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 0.7-9 Index]