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logcondens (version 2.0.2)

Estimate a Log-Concave Probability Density from iid Observations

Description

Given independent and identically distributed observations X(1), ..., X(n), this package allows to compute the maximum likelihood estimator (MLE) of a density as well as a smoothed version of it under the assumption that the density is log-concave, see Rufibach (2007) and Duembgen and Rufibach (2009). The main function of the package is 'logConDens' that allows computation of the log-concave MLE and its smoothed version. In addition, we provide functions to compute (1) the value of the density and distribution function estimates (MLE and smoothed) at a given point (2) the characterizing functions of the estimator, (3) to sample from the estimated distribution, (5) to compute a two-sample permutation test based on log-concave densities, (6) the ROC curve based on log-concave estimates within cases and controls. Finally, three datasets that have been used to illustrate log-concave density estimation are made available.

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Version

Install

install.packages('logcondens')

Monthly Downloads

2,305

Version

2.0.2

License

GPL (>= 2)

Homepage

http://www.biostat.uzh.ch/aboutus/people/rufibach.html

Maintainer

Kaspar Rufibach

Last Published

February 24th, 2011

Functions in logcondens (2.0.2)

activeSetLogCon

Computes a Log-Concave Probability Density Estimate via an Active Set Algorithm

Numerical Routine Q

quantilesLogConDens

Function to compute Quantiles of Fhat

Standard plots for a dlc object

Computes the Integrated Empirical Distribution Function at Arbitrary Real Numbers in s

Numerical Routine J and Some Derivatives

Reliability dataset used to illustrate log-concave density estimation

Summarizing log-concave density estimation

Generate random sample from the log-concave and the smoothed log-concave density estimator

Compute maximal difference between CDFs corresponding to log-concave estimates

Compute ROC curve at a given x based on log-concave estimates for the constituent distributions

activeSetRoutines

Auxiliary Numerical Routines for the Function activeSetLogCon

evaluateLogConDens

Evaluates the Log-Density MLE and Smoothed Estimator at Arbitrary Real Numbers xs

reparametrizations

Changes Between Parametrizations

Robustification and Hermite Interpolation for ICMA

Log-likelihood, New Candidate and Directional Derivative for L

Computes the Integral of the estimated CDF at Arbitrary Real Numbers in s

Compute log-concave density estimator and related quantities

Gradient and Diagonal of Hesse Matrix of Quadratic Approximation to Log-Likelihood Function L

Compute a weighted sample from initial observations

logconTwoSample

Compute p-values for two-sample test based on log-concave CDF estimates

Bright star dataset used to illustrate log-concave density estimation

Data from pancreatic cancer serum biomarker study

Unconstrained piecewise linear MLE

Estimate a Log-Concave Probability Density from iid Observations

Compute ROC curve based on log-concave estimates for the constituent distributions

Quantile Function In a Simple Log-Linear model

Value of the Log-Likelihood Function L, where Input is in Phi-Parametrization

Computes a Log-Concave Probability Density Estimate via an Iterative Convex Minorant Algorithm

Value of the Log-Likelihood Function L, where Input is in Eta-Parametrization

Pool-Adjacent Violaters Algorithm: Least Square Fit under Monotonicity Constraint