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
