# logcondens v2.1.5

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## Estimate a Log-Concave Probability Density from Iid Observations

Given independent and identically distributed observations X(1), ..., X(n), 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, including confidence intervals for given values of false positive fractions (7) computation of a confidence interval for the value of the true density at a fixed point. Finally, three datasets that have been used to illustrate log-concave density estimation are made available.

## Functions in logcondens

 Name Description confIntBootLogConROC_t0 Function to compute a bootstrap confidence interval for the ROC curve at a given t, based on the log-concave ROC curve intECDF Computes the Integrated Empirical Distribution Function at Arbitrary Real Numbers in s Jfunctions Numerical Routine J and Some Derivatives isoMean Pool-Adjacent Violaters Algorithm: Least Square Fit under Monotonicity Constraint evaluateLogConDens Evaluates the Log-Density MLE and Smoothed Estimator at Arbitrary Real Numbers xs brightstar Bright star dataset used to illustrate log-concave density estimation activeSetRoutines Auxiliary Numerical Routines for the Function activeSetLogCon intF Computes the Integral of the estimated CDF at Arbitrary Real Numbers in s Lhat_eta Value of the Log-Likelihood Function L, where Input is in Eta-Parametrization icmaLogCon Computes a Log-Concave Probability Density Estimate via an Iterative Convex Minorant Algorithm Q00 Numerical Routine Q logConCIfunctions Functions that are used by logConCI qloglin Quantile Function In a Simple Log-Linear model plot.dlc Standard plots for a dlc object logcon-package Estimate a Log-Concave Probability Density from iid Observations logConDens Compute log-concave density estimator and related quantities preProcess Compute a weighted sample from initial observations pancreas Data from pancreatic cancer serum biomarker study Local_LL Value of the Log-Likelihood Function L, where Input is in Phi-Parametrization Local_LL_all Log-likelihood, New Candidate and Directional Derivative for L ROCx Compute ROC curve at a given x based on log-concave estimates for the constituent distributions summary.dlc Summarizing log-concave density estimation reliability Reliability dataset used to illustrate log-concave density estimation rlogcon Generate random sample from the log-concave and the smoothed log-concave density estimator reparametrizations Changes Between Parametrizations quadDeriv Gradient and Diagonal of Hesse Matrix of Quadratic Approximation to Log-Likelihood Function L quantilesLogConDens Function to compute Quantiles of Fhat No Results!

## Vignettes of logcondens

 Name plots/-plot1.pdf plots/-plot2.pdf plots/-plot2sample.pdf plots/-plotSimul.pdf plots/-sim1.pdf results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=0.5.txt results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=0.txt results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=1.5.txt results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=1.txt results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=2.txt results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=0.5.txt results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=0.txt results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=1.5.txt results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=1.txt results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=2.txt results/pvals_setting=3_n1=20_n2=25_tau=1.5.txt results/pvals_setting=3_n1=20_n2=25_tau=1.txt results/pvals_setting=3_n1=20_n2=25_tau=2.5.txt results/pvals_setting=3_n1=20_n2=25_tau=2.txt results/pvals_setting=3_n1=20_n2=25_tau=3.txt jss.dtx jsslogo.jpg logcondens.Rnw stat.bib No Results!

## Details

 Type Package Date 2016-07-11 License GPL (>= 2) URL http://www.kasparrufibach.ch , http://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html NeedsCompilation no Packaged 2016-07-13 18:37:23 UTC; rufiback Repository CRAN Date/Publication 2016-07-14 00:31:11
 imports graphics , ks , stats depends R (>= 2.10) Contributors Kaspar Rufibach, Lutz Duembgen