jac.logit: 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).