Title: Maximum Likelihood Estimation of a log-Concave Density Based on
Description: 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>.

Title: Maximum Likelihood Estimation of a Log-Concave Density Based on

Package: logcondens
Type: Package
Title: Estimate a Log-Concave Probability Density from i.i.d. Observations
Version: 1.0
Date: 2006-09-28
Author: Kaspar Rufibach <kaspar.rufibach@stanford.edu> and Lutz Duembgen <duembgen@stat.unibe.ch>
Maintainer: Kaspar Rufibach <kaspar.rufibach@stanford.edu>
Description: Given independent and identically distributed observations X(1), ..., X(n), this package allows to
compute a concave, piecewise linear function phi on [X(1), X(n)] with knots only in {X(1), X(2), ..., X(n)}
such that L(phi) = sum_{i=1}^n W(i)*phi(X(i)) - int_{X(1)}^{X(n)} exp(phi(x)) dx is maximal, for some
weights W(1), ..., W(n) s.t. sum_{i=1}^n W(i) = 1. According to the results in Duembgen and Rufibach (2006),
this function phi maximizes the ordinary log-likelihood sum_{i=1}^n W(i)*phi(X(i))
under the constraint that phi is concave. The corresponding  function exp(phi) is a log-concave probability density.
Two algorithms are offered: An active set algorithm and one based on the pool-adjacent-violaters algorithm.
License: GPL version 2 or newer
URL: www.stanford.edu/~kasparr, www.stat.unibe.ch/~duembgen
Packaged: Thu Sep 28 16:55:30 2006; rufibach

Package: logcondens
Type: Package
Title: Estimate a Log-Concave Probability Density from i.i.d. Observations
Version: 1.1
Date: 2006-10-12
Author: Kaspar Rufibach <kaspar.rufibach@stanford.edu> and Lutz Duembgen <duembgen@stat.unibe.ch>
Maintainer: Kaspar Rufibach <kaspar.rufibach@stanford.edu>
Description: Given independent and identically distributed observations X(1), ..., X(n), this package allows to
compute a concave, piecewise linear function phi on [X(1), X(n)] with knots only in {X(1), X(2), ..., X(n)}
such that L(phi) = sum_{i=1}^n W(i)*phi(X(i)) - int_{X(1)}^{X(n)} exp(phi(x)) dx is maximal, for some
weights W(1), ..., W(n) s.t. sum_{i=1}^n W(i) = 1. According to the results in Duembgen and Rufibach (2006),
this function phi maximizes the ordinary log-likelihood sum_{i=1}^n W(i)*phi(X(i))
under the constraint that phi is concave. The corresponding  function exp(phi) is a log-concave probability density.
Two algorithms are offered: An active set algorithm and one based on the pool-adjacent-violaters algorithm.
License: GPL version 2 or newer
URL: www.stanford.edu/~kasparr, www.stat.unibe.ch/~duembgen
Packaged: Thu Oct 12 16:31:35 2006; rufibach