Visualization and Analysis of Statistical Measures of Confidence
Description
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, (4) calculating the support values and the
probability mass function of the Kaplan-Meier product-limit estimator, and (5) plotting
the actual coverage function associated with a confidence interval for the survivor
function from a randomly right-censored data set. 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 et al. (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(). (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)
. 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(). (5) The km.coverage() function plots the actual coverage function
associated with a confidence interval for the survivor function from a randomly right-censored
data set for one or more of the following confidence intervals: Greenwood, log-minus-log,
Peto, arcsine, and exponential Greenwood. The actual coverage function is plotted for a
small number of items on test, stated coverage, failure rate, and censoring rate. The
km.coverage() function can print an optional table containing all possible
failure/censoring orderings, along with their contribution to the actual coverage function.