The defining equation is
$$\psi = H \times (1-y_1-y_2+H) / ((y_1-H) \times (y_2-H))$$
where
\(P(Y_1 \leq y_1, Y_2 \leq y_2) = H_{\psi}(y_1,y_2)\)
is the cumulative distribution function.
The density function is \(h_{\psi}(y_1,y_2) =\)
$$\psi [1 + (\psi-1)(y_1 + y_2 - 2 y_1 y_2) ] / \left(
[1 + (\psi-1)(y_1 + y_2) ]^2 - 4 \psi
(\psi-1) y_1 y_2 \right)^{3/2}$$
for \(\psi > 0\).
Some writers call \(\psi\) the cross product ratio
but it is called the odds ratio here.
The support of the function is the unit square.
The marginal distributions here are the standard uniform although
it is commonly generalized to other distributions.
If \(\psi = 1\) then
\(h_{\psi}(y_1,y_2) = y_1 y_2\),
i.e., independence.
As the odds ratio tends to infinity one has \(y_1=y_2\).
As the odds ratio tends to 0 one has \(y_2=1-y_1\).
Fisher scoring is implemented using rbiplackcop.
Convergence is often quite slow.