| binom.optim {binom} | R Documentation |
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
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