qloglin

Vector in $[0,1]^d$ where quantiles are to be computed at.

Suppose the random variable $X$ has density function
$$g_\theta(x) = \frac{\theta \exp(\theta x)}{\exp(\theta) - 1}$$ 
for an arbitrary real number $\theta$ and $x \in [0,1]$. The function <code><a rd-options="" href="/link/qloglin?package=logcondens&version=2.1.5" data-mini-rdoc="logcondens::qloglin">qloglin</a></code> is simply the 
 quantile function 
$$G^{-1}_\theta(u) = \theta^{-1} \log \Big( 1 + (e^\theta - 1)u \Big)$$ 
in this model, for $u \in [0,1]$. This quantile function is used for the computation of quantiles of $\widehat F_m$ in <code><a rd-options="" href="/link/quantilesLogConDens?package=logcondens&version=2.1.5" data-mini-rdoc="logcondens::quantilesLogConDens">quantilesLogConDens</a></code>.

htest

nonparametric

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.

Kaspar Rufibach

logcondens

Estimate a Log-Concave Probability Density from Iid Observations

qloglin function

Suppose the random variable $X$ has density function
$$g_\theta(x) = \frac{\theta \exp(\theta x)}{\exp(\theta) - 1}$$ 
for an arbitrary real number $\theta$ and $x \in [0,1]$. The function <code><a rd-options='' href='qloglin'>qloglin</a></code> is simply the 
 quantile function 
$$G^{-1}_\theta(u) = \theta^{-1} \log \Big( 1 + (e^\theta - 1)u \Big)$$ 
in this model, for $u \in [0,1]$. This quantile function is used for the computation of quantiles of $\widehat F_m$ in <code><a rd-options='' href='quantilesLogConDens'>quantilesLogConDens</a></code>.

qloglin: Quantile Function In a Simple Log-Linear model

Description

Usage

Arguments

Value