GNU R estimate a log-concave probability density from Iid observations
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, the package
provides 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.
