binom.optim {binom} R Documentation

## Optimal binomial confidence intervals

### Description

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

### Usage

```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, ...)
```

### Arguments

 `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`.

### Details

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`.

### Value

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.

### Author(s)

Sundar Dorai-Raj (sdorairaj@gmail.com)

`binom.confint`, `binom.plot`, `binom.coverage`, `optim`
```binom.optim(10, k = 1) ## determine optimal significance for x = 0, 10 only