Owen's original paper (page 1077) provides some additional corner cases.
-[: ['T(h, 0) = 0]]
+[expression ['T(h, 0) = 0]]
-[:['T(0, a) = [frac12][pi] arctan(a)]]
+[expression ['T(0, a) = [frac12][pi] arctan(a)]]
-[:['T(h, 1) = [frac12] G(h) \[1 - G(h)\]]]
+[expression ['T(h, 1) = [frac12] G(h) \[1 - G(h)\]]]
-[:['T(h, [infin]) = G(|h|)]]
+[expression ['T(h, [infin]) = G(|h|)]]
where G(h) is the univariate normal with zero mean and unit variance integral from -[infin] to h.
There are also two sets of sanity tests: spot values are computed using __Mathematica and __R.
-
[h4 Implementation]
The function was proposed and evaluated by