Estimate a Log-Concave Probability Density from Iid Observations
Computes a Log-Concave Probability Density Estimate via an Active Set ...
Auxiliary Numerical Routines for the Function activeSetLogCon
Function to compute a bootstrap confidence interval for the ROC curve ...
Evaluates the Log-Density MLE and Smoothed Estimator at Arbitrary Real...
Computes a Log-Concave Probability Density Estimate via an Iterative C...
Computes the Integrated Empirical Distribution Function at Arbitrary R...
Computes the Integral of the estimated CDF at Arbitrary Real Numbers i...
Pool-Adjacent Violaters Algorithm: Least Square Fit under Monotonicity...
Numerical Routine J and Some Derivatives
Value of the Log-Likelihood Function L, where Input is in Eta-Parametr...
Value of the Log-Likelihood Function L, where Input is in Phi-Parametr...
Log-likelihood, New Candidate and Directional Derivative for L
Compute pointwise confidence interval for a density assuming log-conca...
Functions that are used by logConCI
Estimate a Log-Concave Probability Density from iid Observations
Compute log-concave density estimator and related quantities
Compute ROC curve based on log-concave estimates for the constituent d...
Compute p-values for two-sample test based on log-concave CDF estimate...
Compute maximal difference between CDFs corresponding to log-concave e...
Unconstrained piecewise linear MLE
Standard plots for a dlc object
Compute a weighted sample from initial observations
Numerical Routine Q
Quantile Function In a Simple Log-Linear model
Gradient and Diagonal of Hesse Matrix of Quadratic Approximation to Lo...
Function to compute Quantiles of Fhat
Changes Between Parametrizations
Generate random sample from the log-concave and the smoothed log-conca...
Robustification and Hermite Interpolation for ICMA
Compute ROC curve at a given x based on log-concave estimates for the ...
Summarizing log-concave density estimation
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.
Useful links