R: Quantile Function In a Simple Log-Linear model

qloglin {logcondens}

R Documentation

Quantile Function In a Simple Log-Linear model

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.

qloglin(u, t)

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

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

Taylor approximation is used if \theta is small.

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

[Package logcondens version 2.1.8 Index]