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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

$$G^{-1}_\theta(u) = \theta^{-1} \log \Big( 1 + (e^\theta - 1)u \Big)$$

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)

Value

z

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

Arguments

u

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

t

Parameter \(\theta\).