Package: logcondens
Type: Package
Title: Estimate a Log-Concave Probability Density from iid Observations
Version: 1.3.1
Date: 2007-10-04
Author: Kaspar Rufibach <kaspar.rufibach@freesurf.ch> and Lutz Duembgen <duembgen@stat.unibe.ch>
Maintainer: Kaspar Rufibach <kaspar.rufibach@freesurf.ch>
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: http://www.stanford.edu/~kasparr , http://www.stat.unibe.ch/~duembgen
Packaged: Thu Oct  4 14:39:44 2007; rufibach

Package: logcondens
Type: Package
Title: Estimate a Log-Concave Probability Density from iid Observations
Version: 1.3.2
Date: 2008-07-14
Author: Kaspar Rufibach <kaspar.rufibach@gmail.com> and Lutz Duembgen <duembgen@stat.unibe.ch>
Maintainer: Kaspar Rufibach <kaspar.rufibach@gmail.com>
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 (2008),
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: http://www.staff.unibe.ch/duembgen
Packaged: Wed Jul 16 12:47:20 2008; rufibach