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logcondens (version 2.1.8)

Estimate a Log-Concave Probability Density from Iid Observations

Description

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.

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Install

install.packages('logcondens')

Monthly Downloads

1,870

Version

2.1.8

License

GPL (>= 2)

Maintainer

Last Published

August 22nd, 2023

Functions in logcondens (2.1.8)

icmaLogCon

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

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

Compute pointwise confidence interval for a density assuming log-concavity
logConDens

Compute log-concave density estimator and related quantities
confIntBootLogConROC_t0

Function to compute a bootstrap confidence interval for the ROC curve at a given t, based on the log-concave ROC curve
logConROC

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

Functions that are used by logConCI
evaluateLogConDens

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

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

Compute maximal difference between CDFs corresponding to log-concave estimates
isoMean

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

Quantile Function In a Simple Log-Linear model
logconTwoSample

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

Estimate a Log-Concave Probability Density from iid Observations
reparametrizations

Changes Between Parametrizations
quantilesLogConDens

Function to compute Quantiles of Fhat
rlogcon

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

Data from pancreatic cancer serum biomarker study
reliability

Reliability dataset used to illustrate log-concave density estimation
quadDeriv

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

Robustification and Hermite Interpolation for ICMA
plot.dlc

Standard plots for a dlc object
summary.dlc

Summarizing log-concave density estimation
preProcess

Compute a weighted sample from initial observations
Local_LL

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

Auxiliary Numerical Routines for the Function activeSetLogCon
brightstar

Bright star dataset used to illustrate log-concave density estimation
ROCx

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

Log-likelihood, New Candidate and Directional Derivative for L
Jfunctions

Numerical Routine J and Some Derivatives
activeSetLogCon

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

Unconstrained piecewise linear MLE
Lhat_eta

Value of the Log-Likelihood Function L, where Input is in Eta-Parametrization
Q00

Numerical Routine Q