Jfunctions {logcondens}R Documentation

Numerical Routine J and Some Derivatives, to be used by activeSetLogCon

Description

J00 represents the function J(x, y), where for real numbers x, y,

J(x, y) = frac{exp(y) - exp(x)}{y - x}.

Jab gives the respective derivatives, i.e.

J10(x, y) = frac{exp(y) - exp(x) - (y - x) exp(x)}{(y - x)^2};

J11(x, y) = frac{(y - x)(exp(x) + exp(y)) + 2 (exp(y) - exp(x))}{(y - x)^3};

J20(x, y) = 2frac{exp(y) - exp(x) - (y - x)exp(x)-(y - x)^2 exp(x)}{(y - x)^3}.

Usage

J00(x, y)
J10(x, y)
J11(x, y)
J20(x, y)

Arguments

x Arbitrary real number.
y Arbitrary real number.

Value

Value of the respective function.

Note

Taylor approximations are used if y-x is small.

Author(s)

Kaspar Rufibach, kaspar.rufibach@stanford.edu,
http://www.stanford.edu/~kasparr

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


[Package logcondens version 1.0 Index]