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.

Estimate a Log-Concave Probability Density from Iid Observations

Compute MLE of Log-Concave Density on R with Fixed Mode, and
Perform Inference for the Mode.
Computes maximum likelihood estimate of a log-concave density  with fixed and known location of the mode. Performs inference about the mode via a likelihood ratio test. Extension of the logcondens package.

Estimate a Log-Concave Probability Mass function from Discrete
i.i.d. Observations
Kaspar Rufibach <kaspar.rufibach@ifspm.uzh.ch> and Fadoua
Balabdaoui <fadoua@ceremade.dauphine.fr> and Hanna Jankowski
<hkj@mathstat.yorku.ca> and Kathrin Weyermann
<kathrin.weyermann@bkw-fmb.ch>
Given independent and identically distributed observations
X(1), ..., X(n), this package 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, and Rufibach (2011). 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.
http://www.biostat.uzh.ch/aboutus/people/rufibach.html ,
http://www.ceremade.dauphine.fr/~fadoua ,
http://www.math.yorku.ca/~hkj