reparametrizations {logcondens}

Changes Between Parametrizations

Description

Given a vector (\phi_1, \ldots, \phi_m) representing the values of a piecewise linear concave function at x_1, \ldots, x_m, etaphi returns a column vector with the entries

{\bold{\eta}} = \Bigl(\phi_1, \Bigl(\eta_1 + \sum_{j=2}^m (x_i-x_{i-1})\eta_i\Bigr)_{i=2}^m\Bigr).

The function phieta returns a vector with the entries

{\bold{\phi}} = \Bigl(\eta_1, \Bigl(\frac{\phi_i-\phi_{i-1}}{x_i-x_{i-1}}\Bigr)_{i=2}^m\Bigr).

Usage

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

Arguments

x

Vector of independent and identically distributed numbers, with strictly increasing entries.

eta

Vector with entries \eta_i = \eta(x_i).

phi

Vector with entries \phi_i = \phi(x_i).

Note

These functions are not intended to be invoked by the end user.

Author(s)

Kaspar Rufibach, [e-mail],
http://www.kasparrufibach.ch

Lutz Duembgen, [e-mail],
https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html