jac.logit {bisque}

Jacobian for logit transform

Description

Let X=logit(Y) be a transformation of a random variable Y that lies in the closed interval (L,U). This function computes the jacobian J(x) when using the density of Y to evaluate the density of X via

f(x) = f_y(logit^{-1}(x) * (U-L) + L) J(x)

where

J(x) = (U-L) d/dx logit^{-1}(x).

Usage

jac.logit(x, log = TRUE, range = c(0, 1))

Arguments

x

value at which to evaluate J(x)

log

TRUE to return log(J(x))

range

vector specifying min and max range of the closed interval for the logit. While the logit is defined for real numbers in the unit interval, we extend it to real numbers in arbitrary closed intervals (L,U).

Examples

jac.logit(1)