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) , and are detailed in a publication by Weld (2019) . (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().