Visualization and Analysis of Statistical Measures of Confidence
Enables: (1) plotting two-dimensional confidence regions, (2) coverage analysis
of confidence region simulations and (3) calculating confidence intervals and the associated
actual coverage for binomial proportions. Each is given in greater detail next.
(1) Plots the two-dimensional confidence region for probability distribution parameters
(supported distribution suffixes: cauchy, gamma, invgauss, logis, llogis, lnorm, norm, unif,
weibull) corresponding to a user-given complete or right-censored dataset and level of
significance. The crplot() algorithm plots more points in areas of greater curvature to
ensure a smooth appearance throughout the confidence region boundary. An alternative
heuristic plots a specified number of points at roughly uniform intervals along its boundary.
Both heuristics build upon the radial profile log-likelihood ratio technique for plotting
confidence regions given by Jaeger (2016) <10.1080>, and
are detailed in a publication by Weld (2019) <10.1080>.
(2) Performs confidence region coverage simulations for a random sample drawn from a user-
specified parametric population distribution, or for a user-specified dataset and point of
interest with coversim(). (3) Calculates confidence interval bounds for a binomial proportion
with binomTest(), calculates the actual coverage with binomTestCoverage(), and plots the
actual coverage with binomTestCoveragePlot(). Calculates confidence interval bounds for the
binomial proportion using an ensemble of constituent confidence intervals with
binomTestEnsemble(). Calculates confidence interval bounds for the binomial proportion using
a complete enumeration of all possible transitions from one actual coverage acceptance curve
to another which minimizes the root mean square error for n <= 15 and follows the transitions
for well-known confidence intervals for n > 15 using binomTestMSE().10.1080>10.1080>