kmconfband (version 0.1)

noe: Noe Recursions for the Exact Coverage Probability of a Nonparametric Confidence Band for the Survivor Function

Description

This function executes the Noe recursion algorithm for computing the exact coverage probability of a nonparametric confidence band for the survivor function, derived from its single-sample Kaplan-Meier estimate. The calculation relies on two related functions, noe.compute.cgh and noe.compute.pv to execute the necessary recursions.

Usage

noe(tn,ta,tb)

Arguments

tn

a scalar representing the number of individual events that comprise the joint event

ta

an ordered vector of lower endpoints; its length is tn

tb

an ordered vector of tn corresponding upper endpoints

Value

The calculated probability of the joint event, based on the recursions of Noe

References

Jager, L. and Wellner, J. (2005) ``A new goodness of fit test: the reversed Berk-Jones statistic.'' Technical Report 443, Department of Statistics, University of Washington

Noe, M. (1972) ``The calculation of distributions of two-sided Kolmogorov-Smirnov-Type statistics.'' Ann Math Stat 43, 58--64 Shorak, G. R. and Wellner, J. A. (2008) Empirical Processes with Applications to Statistics. Philadelphia, PA: SIAM

See Also

confband, noe.compute.cgh, noe.compute.pv

Examples

## A check of the Noe recursion calculations.  This result is cited in 
## Jager and Wellner's 2005 technical report, Table 1, p. 13.
## The correct value is 0.95

a<-c(0.001340,0.028958,0.114653,0.335379)
b<-c(0.664621,0.885347,0.971042,0.998660)
print(noe(4,a,b))