ReIns (version 1.0.10)

Turnbull: Turnbull estimator

Description

Computes the Turnbull estimator for the survival function of interval censored data.

Usage

Turnbull(x, L, R, censored, trunclower = 0, truncupper = Inf,
         conf.type = "plain", conf.int = 0.95)

Value

A list with following components:

surv

A vector of length length(x) containing the Turnbull estimator evaluated in the elements of x.

fit

The output from the call to survfit.formula, an object of class survfit.

Arguments

x

Vector with points to evaluate the estimator in.

L

Vector of length \(n\) with the lower boundaries of the intervals.

R

Vector of length \(n\) with the upper boundaries of the intervals.

censored

Vector of \(n\) logicals indicating if an observation is interval censored.

trunclower

Lower truncation point, default is 0.

truncupper

Upper truncation point, default is Inf.

conf.type

Type of confidence interval, see survfit.formula. Default is "plain".

conf.int

Confidence level of the two-sided confidence interval, see survfit.formula. Default is 0.95.

Author

Tom Reynkens

Details

We consider the random interval censoring model where one observes \(L \le R\) and where the variable of interest \(X\) lies between \(L\) and \(R\).

Right censored data should be entered as L=l and R=truncupper, and right censored data should be entered as L=trunclower and R=r.

This function calls survfit.formula from survival.

See Section 4.3.2 in Albrecher et al. (2017) for more details.

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

Turnbull, B. W. (1974). "Nonparametric Estimation of a Survivorship Function with Doubly Censored Data." Journal of the American Statistical Association, 69, 169--173.

Turnbull, B. W. (1976). "The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data." Journal of the Royal Statistical Society: Series B (Methodological), 38, 290--295.

See Also

survfit.formula, KaplanMeier

Examples

L <- 1:10
R <- c(1, 2.5, 3, 4, 5.5, 6, 7.5, 8.25, 9, 10.5)
censored <- c(0, 1, 0, 0, 1, 0, 1, 1, 0, 1)

x <- seq(0, 12, 0.1)

# Turnbull estimator
plot(x, Turnbull(x, L, R, censored)$cdf, type="s", ylab="Turnbull estimator")