recnormal1 {VGAM} | R Documentation

## Upper Record Values from a Univariate Normal Distribution

### Description

Maximum likelihood estimation of the two parameters of a univariate normal distribution when the observations are upper record values.

### Usage

    recnormal1(lmean="identity", lsd="loge",
               imean=NULL, isd=NULL, method.init=1, zero=NULL)

### Arguments

`lmean, lsd` | Link functions applied to the mean and sd parameters. See `Links` for more choices.
`imean, isd` | Numeric. Optional initial values for the mean and sd. The default value `NULL` means they are computed internally, with the help of `method.init`.
`method.init` | Integer, either 1 or 2 or 3. Initial method, three algorithms are implemented. Choose the another value if convergence fails, or use `imean` and/or `isd`.
`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

The response must be a vector or one-column matrix with strictly increasing values.

### 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 tries to solve a difficult problem, and the larger the data set the better. Convergence failure can commonly occur, and convergence may be very slow, so set `maxit=200, trace=TRUE`, say. Inputting good initial values are advised.

This family function uses the BFGS quasi-Newton update formula for the working weight matrices. Consequently the estimated variance-covariance matrix may be inaccurate or simply wrong! The standard errors must be therefore treated with caution; these are computed in functions such as `vcov()` and `summary()`.

### Author(s)

T. W. Yee

### References

Arnold, B. C. and Balakrishnan, N. and Nagaraja, H. N. (1998) Records, New York: John Wiley & Sons.

### See Also

`normal1`, `dcnormal1`.

### Examples

    n = 10000
    mymean = 100
    # First value is reference value or trivial record
    rawy = c(mymean, rnorm(n, me=mymean, sd=exp(3)))
    (y = unique(cummax(rawy))) # Keep only observations that are records

    fit = vglm(y ~ 1, recnormal1, trace=TRUE, maxit=200)
    coef(fit, matrix=TRUE)
    Coef(fit)
    summary(fit)

[Package VGAM version 0.7-9 Index]