Based on right or interval censored data, compute the maximum likelihood estimator of a (sub)probability density under the assumption that it is log-concave. For further information see Duembgen, Rufibach and Schuhmacher (2014) <doi:10.1214/14-EJS930>.

Given independent and identically distributed observations X(1), ..., X(n), compute the maximum likelihood estimator (MLE) of a density as well as a smoothed version of it under the assumption that the density is log-concave, see Rufibach (2007) and Duembgen and Rufibach (2009). The main function of the package is 'logConDens' that allows computation of the log-concave MLE and its smoothed version. In addition, we provide functions to compute (1) the value of the density and distribution function estimates (MLE and smoothed) at a given point (2) the characterizing functions of the estimator, (3) to sample from the estimated distribution, (5) to compute a two-sample permutation test based on log-concave densities, (6) the ROC curve based on log-concave estimates within cases and controls, including confidence intervals for given values of false positive fractions (7) computation of a confidence interval for the value of the true density at a fixed point. Finally, three datasets that have been used to illustrate log-concave density estimation are made available.

Given independent and identically distributed observations X(1), ..., X(n), allows to compute the maximum likelihood estimator (MLE) of probability mass function (pmf) under the assumption that it is log-concave, see Weyermann (2007) and Balabdaoui, Jankowski, Rufibach, and Pavlides (2012). The main functions of the package are 'logConDiscrMLE' that allows computation of the log-concave MLE, 'logConDiscrCI' that computes pointwise confidence bands for the MLE, and 'kInflatedLogConDiscr' that computes a mixture of a log-concave PMF and a point mass at k.

A family of three complementary goodness-of-fit tests based on an
    adaptation of Hotelling's T-squared statistic applied to vectors of sample
    log-cumulants (Mellin statistics) for positive-support reliability data.
    The package provides the asymptotic chi-squared reference and parametric
    bootstrap p-values for reliable finite-sample inference, covering the
    Weibull, Frechet, Gamma, Inverse-Gamma, Log-Normal, and Log-Logistic
    families. It also provides three diagnostic diagrams (log-cumulant,
    kurtosis-skewness, and coefficient-of-variation) with bootstrap
    concentration ellipses, in the spirit of moment-ratio diagrams. Methods are
    described in Santos, Ospina, Espinheira and Oliveira (2025).