qloglin {logcondens} | R Documentation |
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 |
Column vector containing the quantiles G_n^{-1}(u_i) for i = 1, ..., d. |
Taylor approximation is used if theta is small.
Kaspar Rufibach, kaspar.rufibach@gmail.com
Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.staff.unibe.ch/duembgen