Turnbull: Turnbull estimator

In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

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)

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.

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.

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.

Author(s)

Tom Reynkens

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")

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.