R: Upper Record Values from a Univariate Normal Distribution

rec.normal {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

    rec.normal(lmean = "identitylink", lsd = "loge",
              imean = NULL, isd = NULL, imethod = 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 `imethod`.
`imethod` | 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` | Can be 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. See `CommonVGAMffArguments` for more information.

### 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

`uninormal`, `double.cens.normal`.

### Examples

    nn <- 10000; mymean <- 100
    # First value is reference value or trivial record
    Rdata <- data.frame(rawy = c(mymean, rnorm(nn, me = mymean, sd = exp(3))))
    # Keep only observations that are records:
    rdata <- data.frame(y = unique(cummax(with(Rdata, rawy))))

    fit <- vglm(y ~ 1, rec.normal, data = rdata, trace = TRUE, maxit = 200)
    coef(fit, matrix = TRUE)
    Coef(fit)
    summary(fit)

[Package VGAM version 1.0-3 Index]