g: Box Cox transformations and related

In andrewzm/atminv: Reproducible package for Section 4.1 of "Spatio-temporal bivariate statistical models for atmospheric trace-gas inversion"

Description

These functions are used to transform from the original space to the the transformed space. In general, if Z are the non-Gaussian observations, then g(Z) is assumed to be Gaussian

Usage

g(Z, lambda)

g_dash(Z, lambda)

g_2dash(Z, lambda)

ginv(Y, lambda)

J_lambda(Z, lambda)

Arguments

Z	the observations (these have to be positive)
lambda	the Box-Cox parameter

Details

The function g is the transformation, g_dash is the derivative of g, g_2dash is the second derivative of g, and ginv is the inverse of g. J_lambda is the Jacobian and is a diagonal matrix with the derivative of g evaluated at the observations as its elements.

Examples

Z <- 1:10 
g(Z,0.4)
g_dash(Z,0.4)
g_2dash(Z,0.4)
J_lambda(Z,0.4)
ginv(g(Z,0.4),0.4)

andrewzm/atminv documentation built on May 10, 2019, 11:14 a.m.