binom.blaker.limits: Blaker's binomial confidence limits
In BlakerCI: Blaker's Binomial and Poisson Confidence Limits

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Fast and accurate calculation of Blaker's binomial confidence limits.

1	binom.blaker.limits(x, n, level = 0.95, tol = 1e-10, ...)

`x`	number of successes.
`n`	number of trials.
`level`	confidence level.
`tol`	numerical tolerance.
`...`	additional arguments to be passed to `binom.blaker.lower.limit`; in fact, just `maxiter` (see `BlakerCI-internal`).

Note that the Blaker's (1 - alpha) confidence interval is the convex hull of the set C of those points where the acceptability function (Blaker (2000)) exceeds level alpha. The original numerical algorithm from Blaker (2000) is prone, when C is a union of disjoint intervals, to skipping a short interval and finding inaccurate over-liberal confidence limits.

Function binom.blaker.limits is, by contrast, immune from such failures and yields always as its result the whole confidence interval (Klaschka (2010)).

Length 2 vector – the lower and upper confidence limits.

Package exactci by M. P. Fay includes another algorithm that calculates Blaker's binomial confidence limits (see user-level function binom.exact and internal function exactbinomCI). It is more sophisticated than the original Blaker's one, but considerably slower and sometimes less accurate than that of binom.blaker.limits.

Earlier 2010 versions of the algorithm of binom.blaker.limits were designed independently of (though already existing) M.P. Fay's packages exact2x2 and exactci. Some later modifications, however, have been inspired by Fay's programs.

Lecoutre & Poitevineau (2014) designed another algorithm for the calculation of the Blaker's confidence limits. Despite more abstract theoretical background and broader scope (not confined to the binomial distribution), it is closely analogous to that of binom.blaker.limits.

Jan Klaschka klaschka@cs.cas.cz

Blaker, H. (2000) Confidence curves and improved exact confidence intervals for discrete distributions. Canadian Journal of Statistics 28: 783-798.
(Corrigenda: Canadian Journal of Statistics 29: 681.)

Klaschka, J. (2010). BlakerCI: An algorithm and R package for the Blaker's binomial confidence limits calculation. Technical report No. 1099, Institute of Computer Science, Academy of Sciences of the Czech Republic, http://hdl.handle.net/11104/0195722.

Lecoutre, B. & Poitevineau J. (2014). New results for computing Blaker's exact confidence interval limits for usual one-parameter discrete distributions. Communications in Statistics - Simulation and Computation, http://dx.doi.org/10.1080/03610918.2014.911900.

`exactci:binom.exact`	One of the options yields Blaker's limits. The algorithm is more sophisti-
	cated than the original Blaker's one.
`propCIs:blakerci`	Implementation of the original algorithm from Blaker (2000).
`binGroup:binBlaker`	Another implementation of the same algorithm.

binom.blaker.limits(3,10) # [1] 0.08726443 0.61941066

## Example of a failure of the original algorithm:
## Requires PropCIs package.
## Tolerance 1e-4 - default in the Blaker's paper.
## Not run: 
blakerci(29,99,conf.level=0.95,tolerance=1e-4) ## [1] 0.2096386 0.3923087
## The correct upper limit should be 0.3929\dots,
## as demonstrated:
## (1) By the same function with a smaller tolerance:
blakerci(29,99,conf.level=0.95,tolerance=1e-7) ## [1] 0.2097022 0.3929079
## (2) By binom.blaker.limits 
##     (default confidence limit 0.95, default tolerance 1e-10):
binom.blaker.limits(29,99) ## [1] 0.2097022 0.3929079
## (3) By exactbinomCI function from package exactci
##     (default confidence level, default tolerance): 
exactbinomCI(29,99,tsmethod="blaker")[1:2] ## [1] 0.2097 0.3929
## The same function, smaller tolerance:
exactbinomCI(29,99,tsmethod="blaker",tol=1e-8)[1:2] 
                                                ## [1] 0.2097022 0.3929079

## Another example of a failure of the original algorithm 
## with even as small tolerance as 1e-6:
blakerci(59,355,conf.level=0.95,tolerance=1e-4) ## [1] 0.1299899 0.2085809
blakerci(59,355,conf.level=0.95,tolerance=1e-5) ## [1] 0.1300799 0.2085409
blakerci(59,355,conf.level=0.95,tolerance=1e-6) ## [1] 0.1300799 0.2085349
## Only for tolerance = 1e-7 the result is satisfactory
## and in agreement with binom.blaker.limits:
blakerci(59,355,conf.level=0.95,tolerance=1e-7) ## [1] 0.1300807 0.2090809
binom.blaker.limits(59,355)                     ## [1] 0.1300807 0.2090809

## End(Not run)