Package: logcondens
Type: Package
Title: Estimate a Log-Concave Probability Density from iid Observations
Version: 1.3.3
Date: 2009-03-04
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 (2009),
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 Mar  4 11:11:21 2009; rufibach

Author: Kaspar Rufibach <kaspar.rufibach@ifspm.uzh.ch> and Lutz
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
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 (2009), 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.

Package: logcondens
Type: Package
Title: Estimate a Log-Concave Probability Density from iid Observations
Version: 1.3.5
Date: 2009-12-07
Author: Kaspar Rufibach <kaspar.rufibach@ifspm.uzh.ch> and Lutz
Duembgen <duembgen@stat.unibe.ch>
Maintainer: Kaspar Rufibach <kaspar.rufibach@ifspm.uzh.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 (2009), 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 to compute the estimator:
An active set algorithm and one based on the
pool-adjacent-violaters algorithm. In addition, we provide
functions to compute (1) the value of the density and
distribution function estimate at a given point (2) a smoothed
log-concave density estimator (3) the characterizing functions
of the estimator and (4) to sample from the estimated
distribution. Finally, two datasets that have been used to
illustrate log-concave density estimation are made available.
License: GPL (>= 2)
URL: http://www.biostat.uzh.ch/aboutus/people/rufibach.html,
http://www.staff.unibe.ch/duembgen
Packaged: 2009-12-07 10:11:12 UTC; rufibach
Repository: CRAN
Date/Publication: 2009-12-07 10:53:55