logcondens (version 2.1.8)

qloglin: 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

$$G_{\theta }^{-1}(u)={\theta }^{-1}\log (1+(e^{\theta }-1)u)$$

in this model, for $u\in [0,1]$. This quantile function is used for the computation of quantiles of ${\hat{F}}_m$ in quantilesLogConDens.

Usage

qloglin(u, t)

Value

z

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

Arguments

u

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

t

Parameter $\theta$.

Author

Kaspar Rufibach, ,
http://www.kasparrufibach.ch

Lutz Duembgen, ,
https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html