logcondens: Estimate a Log-Concave Probability Density from iid Observations
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.
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Reverse dependencies: