binom.optim: Optimal binomial confidence intervals
In binom: Binomial Confidence Intervals For Several Parameterizations

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

Uses optimization to minimize the integrated mean squared error between the calculated coverage and the desired confidence level for a given binomial confidence interval.

binom.optim(n, conf.level = 0.95, method = binom.lrt,
            k = n%/%2 + 1, p0 = 0, transform = TRUE,
            plot = FALSE, tol = .Machine$double.eps^0.5,
            start = NULL, ...)

`n`	The number of independent trials in the binomial experiment.
`conf.level`	The level of confidence to be used in the confidence interval.
`method`	The method used to estimate the confidence interval.
`k`	See Details.
`p0`	The minimum probability of success to allow in the optimization. See Details.
`transform`	logical; If `TRUE` the optimizer will do an unconstrained optimization on the signficance probability in the logit space.
`plot`	logical; If `TRUE` the results are sent to `binom.plot`.
`tol`	The minimum significance level to allow in the optimization. See Details.
`start`	A starting value on the optimal confidence level.
`...`	Additional arguments to pass to `optim`.

This function minimizes the squared error between the expected coverage probability and the desired confidence level.

alpha[opt]=argmin[alpha] integral[C(p,n)-(1-alpha)]^2dp

The optimizer will adjust confidence intervals for all x = 0 to n depending on the value of k provided. If k is one, only the confidence levels for x = 0 and n are adjusted. If k = [n/2] then all confidence intervals are adjusted. This assumes the confidence intervals are the same length for x = x[k] and x[n - k + 1], which is the case for all methods provided in this package except binom.cloglog.

A list with the following elements:

`par`	Final confidence levels. The length of this vector is `k`.
`value`	The final minimized value from `optim`.
`counts`	The number of function and gradient calls from `optim`.
`convergence`	Convergence code from `optim`.
`message`	Any message returned by the L-BFGS-B or BFGS optimizer.
`confint`	A `data.frame` returned from a call to `method` using the optimized confidence levels.

Sundar Dorai-Raj (sdorairaj@gmail.com)

binom.confint, binom.plot, binom.coverage, optim

1 2	binom.optim(10, k = 1) ## determine optimal significance for x = 0, 10 only binom.optim(3, method = binom.wilson) ## determine optimal significance for all x