reparametrizations {logcondens}R Documentation

Changes Between Parametrizations

Description

Given a vector (varphi_1, ..., varphi_m) representing the values of a piecewise linear concave function at x_1, ..., x_m, etaphi returns a column vector with the entries

{eta} = Bigl(varphi_1, Bigl(eta_1 + sum_{j=2}^m (x_i-x_{i-1})eta_iBigr)_{i=2}^mBigr).

The function phieta returns a vector with the entries

{varphi} = Bigl(eta_1, Bigl(frac{varphi_i-varphi_{i-1}}{x_i-x_{i-1}}Bigr)_{i=2}^mBigr).

Usage

etaphi(x, eta)
phieta(x, phi)

Arguments

x Vector of independent and identically distributed numbers, with strictly increasing entries.
eta Column vector with entries eta_i = eta(x_i).
phi Column vector with entries varphi_i = varphi(x_i).

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]