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, 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.



  • Minor updates.


  • Properly import globals.


  • Added proper S3 exporting.


  • Updated dependency for c2hat.
  • Updated webadress for Lutz Duembgen.


  • Updated logConCI to compute a confidence interval.


  • Reorganized vignette to conform.
  • Updated references.


  • Added seed to logConCI.Rd.
  • Changed handling of pmax in logConCI().


  • Corrected a wrong link in evaluateLogConDens.
  • Added the function logConCI, contributed by M. Azadbakhsh and H. Jankowski.
  • Updated references.


  • Updated package to pass new checks on CRAN.
  • Updated references.


  • Modified function logConROC (option "smooth").
  • Added function confIntBootLogConROC_t0().


  • Added NAMESPACE.


  • Updated some references.
  • Corrected minor typos.


  • Contains final JSS paper version.


  • Added functions ROCx() and logConROC()
  • Added dataset 'pancreas'


  • Revision according to reviewer comments for JSS paper.
  • Replaced 'vectorToString()' by 'paste()' using option 'collapse'
  • Added JSS paper as a vignette to the package


  • Substantially reworked version according to revision of paper Duembgen and Rufibach (2010).
  • Updated Taylor approximations according to technical report Duembgen et al (2010).


  • Added 'reliability' and 'brightstar' datasets.
  • Added 'logconSmoothed'.
  • Added 'rlogcon'.


  • Included vignette in the package.


  • Updated references.
  • Updated vignette.


  • Updated references.


  • Updated contact informations.


  • Modified quantilesLogConDens. Value for p0 > 1 is set to +Inf.
  • Added the functions intF and intECDF.
  • Updated references.


  • Simplified evaluateLogConDens and quantilesLogConDens. Therefore, J00 was slightly generalized to variable upper endpoint and the function qloglin was introduced.
  • Replaced the variable name F for the estimated distribution function by Fhat.
  • Shortened title.


  • Specified affiliations.
  • Indicated that MatLab files are available upon request from Lutz Duembgen.
  • MLE: printed only L, but needs to print L_new; and print = 1 replaced by print = TRUE.
  • icmaLogCon: replaced ambiguous option "robust" by "robustif" (there is already a function called "robust")
  • LocalMLE: replaced explicit calculations by function call to LocalConvexity.
  • Help files: reformulated and complemented some entries.
  • Vignette: corrected some typos.

logcondens_1.0 (initial version):

  • Provide functions to estimate a log-concave probability density.

Reference manual

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2.1.6 by Kaspar Rufibach, 12 days ago ,

Browse source code at

Authors: Kaspar Rufibach <[email protected]> and Lutz Duembgen <[email protected]>

Documentation:   PDF Manual  

GPL (>= 2) license

Imports ks, graphics, stats

Depended on by logcondens.mode, smoothtail.

Suggested by logconcens, pROC.

See at CRAN