qloglin: Quantile Function In a Simple Log-Linear model

In logcondens: Estimate a Log-Concave Probability Density from Iid Observations

Quantile Function In a Simple Log-Linear model

Description

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 qloglin 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 quantilesLogConDens.

Usage

qloglin(u, t)

Arguments

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

Value

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

Note

Taylor approximation is used if \theta is small.

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

Author(s)

Kaspar Rufibach, [e-mail],
http://www.kasparrufibach.ch

Lutz Duembgen, [e-mail],
https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html

logcondens documentation built on Aug. 22, 2023, 5:06 p.m.