conf

Enables: (1) plotting two-dimensional confidence regions, (2) coverage analysis of confidence region simulations, (3) calculating confidence intervals and the associated actual coverage for binomial proportions, and (4) calculating the support values and the probability mass function of the Kaplan-Meier product-limit estimator. 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) doi:10.1080/00031305.2016.1182946, and are detailed in a publication by Weld et al. (2019) doi:10.1080/00031305.2018.1564696. (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(). (4) The km.support() function calculates the support values of the Kaplan-Meier product-limit estimator for a given sample size n using an induction algorithm described in Qin et al. (2023) doi:10.1080/00031305.2022.2070279. The km.outcomes() function generates a matrix containing all possible outcomes (all possible sequences of failure times and right-censoring times) of the value of the Kaplan-Meier product-limit estimator for a particular sample size n. The km.pmf() function generates the probability mass function for the support values of the Kaplan-Meier product-limit estimator for a particular sample size n, probability of observing a failure h at the time of interest expressed as the cumulative probability percentile associated with X = min(T, C), where T is the failure time and C is the censoring time under a random-censoring scheme. The km.surv() function generates multiple probability mass functions of the Kaplan-Meier product-limit estimator for the same arguments as those given for km.pmf().