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  "Type": "Package",
  "Title": "Estimate a Log-Concave Probability Density from Iid Observations",
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  "Date": "2026-04-26",
  "Authors@R": "c(person(given = \"Kaspar\", family = \"Rufibach\", role = c(\"aut\", \"cre\"), email = \"kaspar.rufibach@gmail.com\"),\nperson(given = \"Duembgen\", family = \"Lutz\", role = \"aut\", email = \"duembgen@stat.unibe.ch\"))",
  "Maintainer": "Kaspar Rufibach <kaspar.rufibach@gmail.com>",
  "Description": "Given independent and identically distributed observations\nX(1), ..., X(n), compute the maximum likelihood estimator (MLE)\nof a density as well as a smoothed version of it under the\nassumption that the density is log-concave, see Rufibach (2007)\nand Duembgen and Rufibach (2009). The main function of the\npackage is 'logConDens' that allows computation of the\nlog-concave MLE and its smoothed version. In addition, we\nprovide functions to compute (1) the value of the density and\ndistribution function estimates (MLE and smoothed) at a given\npoint (2) the characterizing functions of the estimator, (3) to\nsample from the estimated distribution, (5) to compute a\ntwo-sample permutation test based on log-concave densities, (6)\nthe ROC curve based on log-concave estimates within cases and\ncontrols, including confidence intervals for given values of\nfalse positive fractions (7) computation of a confidence\ninterval for the value of the true density at a fixed point.\nFinally, three datasets that have been used to illustrate\nlog-concave density estimation are made available.",
  "License": "GPL (>= 2)",
  "URL": "http://www.kasparrufibach.ch ,\nhttps://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html",
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  "Author": "Kaspar Rufibach [aut, cre], Duembgen Lutz [aut]",
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  "_exports": [
    "activeSetLogCon",
    "c2hat",
    "confIntBootLogConROC_t0",
    "etaphi",
    "evaluateLogConDens",
    "ftilde",
    "icmaLogCon",
    "intECDF",
    "intF",
    "isoMean",
    "J00",
    "J10",
    "J11",
    "J20",
    "Lhat_eta",
    "Local_LL",
    "Local_LL_all",
    "LocalCoarsen",
    "LocalConvexity",
    "LocalExtend",
    "LocalF",
    "LocalMLE",
    "LocalNormalize",
    "LocalVariance",
    "logConCI",
    "logConDens",
    "logConROC",
    "logconTwoSample",
    "maxDiffCDF",
    "MLE",
    "phieta",
    "plot.dlc",
    "preProcess",
    "Q00",
    "qloglin",
    "quadDeriv",
    "quantilesLogConDens",
    "rlogcon",
    "robust",
    "ROCx",
    "summary.dlc"
  ],
  "_datasets": [
    {
      "name": "brightstar",
      "title": "Bright star dataset used to illustrate log-concave density estimation",
      "object": "brightstar",
      "file": "brightstar.rda",
      "class": [
        "data.frame"
      ],
      "fields": [
        "nr",
        "rad",
        "rot"
      ],
      "rows": 9110,
      "table": true,
      "tojson": true
    },
    {
      "name": "pancreas",
      "title": "Data from pancreatic cancer serum biomarker study",
      "object": "pancreas",
      "file": "pancreas.rda",
      "class": [
        "data.frame"
      ],
      "fields": [
        "ca199",
        "ca125",
        "status"
      ],
      "rows": 141,
      "table": true,
      "tojson": true
    },
    {
      "name": "reliability",
      "title": "Reliability dataset used to illustrate log-concave density estimation",
      "object": "reliability",
      "file": "reliability.rda",
      "class": [
        "numeric"
      ],
      "fields": [],
      "table": false,
      "tojson": true
    }
  ],
  "_help": [
    {
      "page": "logcondens-package",
      "title": "Estimate a Log-Concave Probability Density from iid Observations",
      "topics": [
        "logcondens-package",
        "log-concave",
        "logcon",
        "logcondens"
      ]
    },
    {
      "page": "activeSetLogCon",
      "title": "Computes a Log-Concave Probability Density Estimate via an Active Set Algorithm",
      "topics": [
        "activeSet",
        "activeSetLogCon"
      ]
    },
    {
      "page": "activeSetRoutines",
      "title": "Auxiliary Numerical Routines for the Function activeSetLogCon",
      "topics": [
        "activeSetRoutines",
        "LocalCoarsen",
        "LocalConvexity",
        "LocalExtend",
        "LocalF",
        "LocalMLE",
        "LocalNormalize",
        "LocalVariance"
      ]
    },
    {
      "page": "brightstar",
      "title": "Bright star dataset used to illustrate log-concave density estimation",
      "topics": [
        "brightstar"
      ]
    },
    {
      "page": "confIntBootLogConROC_t0",
      "title": "Function to compute a bootstrap confidence interval for the ROC curve at a given t, based on the log-concave ROC curve",
      "topics": [
        "confIntBootLogConROC_t0"
      ]
    },
    {
      "page": "evaluateLogConDens",
      "title": "Evaluates the Log-Density MLE and Smoothed Estimator at Arbitrary Real Numbers xs",
      "topics": [
        "evaluateLogConDens"
      ]
    },
    {
      "page": "icmaLogCon",
      "title": "Computes a Log-Concave Probability Density Estimate via an Iterative Convex Minorant Algorithm",
      "topics": [
        "icmaLogCon"
      ]
    },
    {
      "page": "intECDF",
      "title": "Computes the Integrated Empirical Distribution Function at Arbitrary Real Numbers in s",
      "topics": [
        "intECDF"
      ]
    },
    {
      "page": "intF",
      "title": "Computes the Integral of the estimated CDF at Arbitrary Real Numbers in s",
      "topics": [
        "intF"
      ]
    },
    {
      "page": "isoMean",
      "title": "Pool-Adjacent Violaters Algorithm: Least Square Fit under Monotonicity Constraint",
      "topics": [
        "isoMean"
      ]
    },
    {
      "page": "Jfunctions",
      "title": "Numerical Routine J and Some Derivatives",
      "topics": [
        "J00",
        "J10",
        "J11",
        "J20",
        "Jfunctions"
      ]
    },
    {
      "page": "Lhat_eta",
      "title": "Value of the Log-Likelihood Function L, where Input is in Eta-Parametrization",
      "topics": [
        "Lhat_eta"
      ]
    },
    {
      "page": "Local_LL",
      "title": "Value of the Log-Likelihood Function L, where Input is in Phi-Parametrization",
      "topics": [
        "Local_LL"
      ]
    },
    {
      "page": "Local_LL_all",
      "title": "Log-likelihood, New Candidate and Directional Derivative for L",
      "topics": [
        "Local_LL_all"
      ]
    },
    {
      "page": "logConCI",
      "title": "Compute pointwise confidence interval for a density assuming log-concavity",
      "topics": [
        "logConCI"
      ]
    },
    {
      "page": "logConCIfunctions",
      "title": "Functions that are used by logConCI",
      "topics": [
        "c2hat",
        "ftilde",
        "logConCIfunctions",
        "rLCD"
      ]
    },
    {
      "page": "logConDens",
      "title": "Compute log-concave density estimator and related quantities",
      "topics": [
        "logConDens"
      ]
    },
    {
      "page": "logConROC",
      "title": "Compute ROC curve based on log-concave estimates for the constituent distributions",
      "topics": [
        "logConROC"
      ]
    },
    {
      "page": "logconTwoSample",
      "title": "Compute p-values for two-sample test based on log-concave CDF estimates",
      "topics": [
        "logconTwoSample"
      ]
    },
    {
      "page": "maxDiffCDF",
      "title": "Compute maximal difference between CDFs corresponding to log-concave estimates",
      "topics": [
        "maxDiffCDF"
      ]
    },
    {
      "page": "MLE",
      "title": "Unconstrained piecewise linear MLE",
      "topics": [
        "MLE"
      ]
    },
    {
      "page": "pancreas",
      "title": "Data from pancreatic cancer serum biomarker study",
      "topics": [
        "pancreas"
      ]
    },
    {
      "page": "plot.dlc",
      "title": "Standard plots for a dlc object",
      "topics": [
        "plot.dlc"
      ]
    },
    {
      "page": "preProcess",
      "title": "Compute a weighted sample from initial observations",
      "topics": [
        "preProcess"
      ]
    },
    {
      "page": "Q00",
      "title": "Numerical Routine Q",
      "topics": [
        "Q00"
      ]
    },
    {
      "page": "qloglin",
      "title": "Quantile Function In a Simple Log-Linear model",
      "topics": [
        "qloglin"
      ]
    },
    {
      "page": "quadDeriv",
      "title": "Gradient and Diagonal of Hesse Matrix of Quadratic Approximation to Log-Likelihood Function L",
      "topics": [
        "quadDeriv"
      ]
    },
    {
      "page": "quantilesLogConDens",
      "title": "Function to compute Quantiles of Fhat",
      "topics": [
        "quantilesLogConDens"
      ]
    },
    {
      "page": "reliability",
      "title": "Reliability dataset used to illustrate log-concave density estimation",
      "topics": [
        "reliability"
      ]
    },
    {
      "page": "reparametrizations",
      "title": "Changes Between Parametrizations",
      "topics": [
        "etaphi",
        "phieta",
        "reparametrizations"
      ]
    },
    {
      "page": "rlogcon",
      "title": "Generate random sample from the log-concave and the smoothed log-concave density estimator",
      "topics": [
        "rlogcon"
      ]
    },
    {
      "page": "robust",
      "title": "Robustification and Hermite Interpolation for ICMA",
      "topics": [
        "robust"
      ]
    },
    {
      "page": "ROCx",
      "title": "Compute ROC curve at a given x based on log-concave estimates for the constituent distributions",
      "topics": [
        "ROCx"
      ]
    },
    {
      "page": "summary.dlc",
      "title": "Summarizing log-concave density estimation",
      "topics": [
        "summary.dlc"
      ]
    }
  ],
  "_rundeps": [
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    "kernlab",
    "KernSmooth",
    "ks",
    "lattice",
    "Matrix",
    "mclust",
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  "_vignettes": [
    {
      "source": "logcondens.Rnw",
      "filename": "logcondens.pdf",
      "title": "logcondens: Computations Related to Univariate Log-Concave Density Estimation (Duembgen and Rufibach, 2011, Journal of Statistical Software, 39(6), 1-28.)",
      "engine": "utils::Sweave",
      "headings": [
        "Introduction",
        "Computing the log-concave estimator",
        "Characterization and properties of the estimator",
        "Smoothing the log-concave density estimator",
        "Implementation and main functions",
        "Sampling from the different estimators",
        "Illustration of main functions on simulated example",
        "Exemplary analysis of reliability dataset",
        "Smooth two-sample permutation test",
        "Final remarks",
        "Density, distribution and quantile function",
        "The integral of F at an arbitrary x0",
        "The smoothed log-concave density estimator",
        "The smoothed log-concave CDF estimator",
        "Computation of the two-sample test statistic"
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