# 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 | |

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## Vignettes of logcondens

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## 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 |

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