cgumbel {VGAM} | R Documentation

## Censored Gumbel Distribution

### Description

Maximum likelihood estimation of the 2-parameter Gumbel distribution when there are censored observations. A matrix response is not allowed.

### Usage

    cgumbel(llocation="identity", lscale = "loge",
            elocation = list(), escale = list(), iscale=NULL,
            mean=TRUE, percentiles=NULL, zero=2)

### Arguments

`llocation, lscale` | Character. Parameter link functions for the location and (positive) scale parameters. See `Links` for more choices.
`elocation, escale` | Extra argument for the respective links. See `earg` in `Links` for general information.
`iscale` | Numeric and positive. Initial value for scale. Recycled to the appropriate length. In general, a larger value is better than a smaller value. The default is to choose the value internally.
`mean` | Logical. Return the mean? If `TRUE` then the mean is returned, otherwise percentiles given by the `percentiles` argument.
`percentiles` | Numeric with values between 0 and 100. If `mean=FALSE` then the fitted values are percentiles which must be specified by this argument.
`zero` | An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The value (possibly values) must be from the set {1,2} corresponding respectively to location and scale. If `zero=NULL` then all linear/additive predictors are modelled as a linear combination of the explanatory variables. The default is to fit the shape parameter as an intercept only.

### Details

This VGAM family function is like `gumbel` but handles observations that are left-censored (so that the true value would be less than the observed value) else right-censored (so that the true value would be greater than the observed value). To indicate which type of censoring, input `extra = list(leftcensored = vec1, rightcensored = vec2)` where `vec1` and `vec2` are logical vectors the same length as the response. If the two components of this list are missing then the logical values are taken to be `FALSE`. The fitted object has these two components stored in the `extra` slot.

### Value

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

### Warning

Numerical problems may occur if the amount of censoring is excessive.

### Note

See `gumbel` for details about the Gumbel distribution. The initial values are based on assuming all uncensored observations, therefore could be improved upon.

### Author(s)

T. W. Yee

### References

Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.

### See Also

`gumbel`, `egumbel`, `rgumbel`, `guplot`, `gev`, `venice`.

### Examples

    # Example 1
    ystar = venice[["r1"]]  # Use the first order statistic as the response
    n = length(ystar)
    L = runif(n, 100, 104) # Lower censoring points
    U = runif(n, 130, 135) # Upper censoring points
    y = pmax(L, ystar) # Left  censored
    y = pmin(U, y)     # Right censored
    extra = list(leftcensored = ystar < L, rightcensored = ystar > U)
    fit = vglm(y ~ scale(year), data=venice, trace=TRUE, extra=extra,
               cgumbel(mean=FALSE, perc=c(5,25,50,75,95)))
    coef(fit, matrix=TRUE)
    head(fitted(fit))
    fit@extra

    # Example 2: simulated data
    n = 1000
    ystar = rgumbel(n, loc=1, scale=exp(0.5)) # The uncensored data
    L = runif(n, -1, 1) # Lower censoring points
    U = runif(n,  2, 5) # Upper censoring points
    y = pmax(L, ystar) # Left  censored
    y = pmin(U, y)     # Right censored
    ## Not run: par(mfrow=c(1,2)); hist(ystar); hist(y);
    extra = list(leftcensored = ystar < L, rightcensored = ystar > U)
    fit = vglm(y ~ 1, trace=TRUE, extra=extra, cgumbel)
    coef(fit, matrix=TRUE)

[Package VGAM version 0.7-9 Index]