qloglin {logcondens}R Documentation

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 Column vector containing the quantiles G_n^{-1}(u_i) for i = 1, ..., d.

Note

Taylor approximation is used if theta is small.

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com

Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.staff.unibe.ch/duembgen


[Package logcondens version 1.3.3 Index]