VGAM: cens.gumbel – R documentation

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cens.gumbel

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

cens.gumbel(llocation = "identitylink", lscale = "loglink", iscale = NULL,
            mean = TRUE, percentiles = NULL, zero = "scale")

Arguments

`llocation, lscale`	Character. Parameter link functions for the location and (positive) scale parameters. See `Links` for more choices.
`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.

Examples

# Example 1
ystar <- venice[["r1"]]  # Use the first order statistic as the response
nn <- length(ystar)
L <- runif(nn, 100, 104)  # Lower censoring points
U <- runif(nn, 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,
            fam = cens.gumbel(mean = FALSE, perc = c(5, 25, 50, 75, 95)))
coef(fit, matrix = TRUE)
head(fitted(fit))
fit@extra

# Example 2: simulated data
nn <- 1000
ystar <- rgumbel(nn, loc = 1, scale = exp(0.5))  # The uncensored data
L <- runif(nn, -1, 1)  # Lower censoring points
U <- runif(nn,  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, fam = cens.gumbel)
coef(fit, matrix = TRUE)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13