logcondens (version 2.0.2)

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 $\widehat F_m$ 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 $i = 1, \ldots, d$.