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

Description

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

Usage

 ```1 2``` ```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 ≤ 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`.

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.

`survfit.formula`, `KaplanMeier`

Examples

 ```1 2 3 4 5 6 7 8``` ```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") ```

Example output

```
```

ReIns documentation built on July 2, 2020, 4:03 a.m.