Tetrachoric Function

The function defined by

$\begin{displaymath} T_n(x)\equiv {(-1)^{n-1}\over\sqrt{n!}} Z^{(n-1)}(x), \end{displaymath}$

where

$\begin{displaymath} Z(x)= {1\over\sqrt{2\pi}} e^{-x^2/2} \end{displaymath}$

and $Z^{(k)}(x)$ is the

th derivative of

See also Normal Distribution

References

Kenney, J. F. and Keeping, E. S. ``Tetrachoric Correlation.'' §8.5 in Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 205-207, 1951.