## A Generalized Plackett TVT Formula

A generalization of Plackett's formula requires . If definition (23) is used for , then

so Plackett's TVN formula (12) can be applied, giving

If the inner integral is transformed using , the exponential terms are combined, a second change of variables is used, and the order of integration is reversed, the result is

Next, the factorization is used, along with the inner integral value , and some algebra, to obtain

The final change of variables, , and some more algebra, produces the new trivariate t formula

This can be written in a form very similar to the form for equation (12) as
 (24)

Appropriate permutations of the 's and the 's can be used to provide similar formulas for and .

2004-04-13