dcnormal1 {VGAM} | R Documentation

## Univariate Normal Distribution with Double Censoring

### Description

Maximum likelihood estimation of the two parameters of a univariate normal distribution when there is double censoring.

### Usage

    dcnormal1(r1 = 0, r2 = 0, link.sd = "loge",
              earg=list(), isd = NULL, zero = NULL)

### Arguments

`r1, r2` | Integers. Number of smallest and largest values censored, respectively.
`link.sd` | Parameter link function applied to the standard deviation. See `Links` for more choices. Being a positive quantity, a log link is the default.
`earg` | List. Extra argument for the link. See `earg` in `Links` for general information.
`isd` | Numeric. Initial value for the standard deviation. The default value `NULL` means an initial value is obtained internally from the data.
`zero` | An integer with 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

This family function uses the Fisher information matrix given in Harter and Moore (1966). The matrix is not diagonal if either `r1` or `r2` are positive.

By default, the mean is the first linear/additive predictor and the log of the standard deviation is the second linear/additive predictor.

### Value

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

### Note

This family function only handles a vector or one-column matrix response. The `weights` argument, if used, are interpreted as frequencies, therefore it must be a vector with positive integer values.

With no censoring at all (the default), it is better (and equivalent) to use `normal1`.

### Author(s)

T. W. Yee

### References

Harter, H. L. and Moore, A. H. (1966) Iterative maximum-likelihood estimation of the parameters of normal populations from singly and doubly censored samples. Biometrika, 53, 205–213.

### See Also

`normal1`, `tobit`.

### Examples

    ## Not run:
    # Repeat the simulations described in Harter and Moore (1966)
    SIMS = 100   # Number of simulations (change this to 1000)
    mu.save = sd.save = rep(NA, len=SIMS)
    r1 = 0; r2 = 4; n = 20
    for(sim in 1:SIMS) {
        y = sort(rnorm(n))
        y = y[(1+r1):(n-r2)]  # Delete r1 smallest and r2 largest
        fit = vglm(y ~ 1, dcnormal1(r1=r1, r2=r2))
        mu.save[sim] = predict(fit)[1,1]
        sd.save[sim] = exp(predict(fit)[1,2])   # Assumes a log link and ~ 1
    }
    # Now look at the results
    c(mean(mu.save), mean(sd.save))  # Should be c(0,1)
    c(sd(mu.save), sd(sd.save))
    ## End(Not run)

    # Data from Sarhan and Greenberg (1962); MLEs are mu=9.2606, sd=1.3754
    strontium90 = c(8.2, 8.4, 9.1, 9.8, 9.9)
    fit = vglm(strontium90 ~ 1, dcnormal1(r1=2, r2=3, isd=6), trace=TRUE)
    coef(fit, matrix=TRUE)
    Coef(fit)

[Package VGAM version 0.7-9 Index]