survival (version 3.1-8)

dsurvreg: Distributions available in survreg.

Description

Density, cumulative distribution function, quantile function and random generation for the set of distributions supported by the survreg function.

Usage

dsurvreg(x, mean, scale=1, distribution='weibull', parms)
psurvreg(q, mean, scale=1, distribution='weibull', parms)
qsurvreg(p, mean, scale=1, distribution='weibull', parms)
rsurvreg(n, mean, scale=1, distribution='weibull', parms)

Arguments

x

vector of quantiles. Missing values (NAs) are allowed.

q

vector of quantiles. Missing values (NAs) are allowed.

p

vector of probabilities. Missing values (NAs) are allowed.

n

number of random deviates to produce

mean

vector of linear predictors for the model. This is replicated to be the same length as p, q or n.

scale

vector of (positive) scale factors. This is replicated to be the same length as p, q or n.

distribution

character string giving the name of the distribution. This must be one of the elements of survreg.distributions

parms

optional parameters, if any, of the distribution. For the t-distribution this is the degrees of freedom.

Value

density (dsurvreg), probability (psurvreg), quantile (qsurvreg), or for the requested distribution with mean and scale parameters mean and sd.

Details

Elements of q or p that are missing will cause the corresponding elements of the result to be missing.

The location and scale values are as they would be for survreg. The label "mean" was an unfortunate choice (made in mimicry of qnorm); since almost none of these distributions are symmetric it will not actually be a mean, but corresponds instead to the linear predictor of a fitted model. Translation to the usual parameterization found in a textbook is not always obvious. For example, the Weibull distribution is fit using the Extreme value distribution along with a log transformation. Letting \(F(t) = 1 - \exp[-(at)^p]\) be the cumulative distribution of the Weibull using a standard parameterization in terms of \(a\) and \(p\), the survreg location corresponds to \(-\log(a)\) and the scale to \(1/p\) (Kalbfleisch and Prentice, section 2.2.2).

References

Kalbfleisch, J. D. and Prentice, R. L. (1970). The Statistical Analysis of Failure Time Data Wiley, New York.

See Also

survreg, Normal

Examples

# NOT RUN {
# List of distributions available
names(survreg.distributions)
# }
# NOT RUN {
 [1] "extreme"     "logistic"    "gaussian"    "weibull"     "exponential"
 [6] "rayleigh"    "loggaussian" "lognormal"   "loglogistic" "t"          
# }
# NOT RUN {
# Compare results
all.equal(dsurvreg(1:10, 2, 5, dist='lognormal'), dlnorm(1:10, 2, 5))

# Hazard function for a Weibull distribution
x   <- seq(.1, 3, length=30)
haz <- dsurvreg(x, 2, 3)/ (1-psurvreg(x, 2, 3))
# }
# NOT RUN {
plot(x, haz, log='xy', ylab="Hazard") #line with slope (1/scale -1)
# }