# qloglin: Quantile Function In a Simple Log-Linear model In logcondens: Estimate a Log-Concave Probability Density from Iid Observations

## Description

Suppose the random variable X has density function

g_θ(x) = (θ exp(θ x))/(exp(θ) - 1)

for an arbitrary real number θ and x \in [0,1]. The function qloglin is simply the quantile function

G^{-1}_θ(u) = θ^{-1} log (1 + (e^θ - 1)u)

in this model, for u \in [0,1]. This quantile function is used for the computation of quantiles of \widehat F_m in quantilesLogConDens.

## Usage

 1 qloglin(u, t) 

## Arguments

 u Vector in [0,1]^d where quantiles are to be computed at. t Parameter θ.

## Value

 z Vector containing the quantiles G_n^{-1}(u_i) for i = 1, …, d.

## Note

Taylor approximation is used if θ is small.

This function is not intended to be called by the end user.

## Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

logcondens documentation built on May 2, 2019, 6:11 a.m.