Approximation Error

Since $\vert I_{m,n+q} \vert < L^{-q} \vert I_{m,n} \vert$ for $F > L$, the relative error in $I_{m,n+q}$ is bounded by

$$\vert \epsilon_q \vert < (-1)^q(\frac{D_2}{D_1})^q\left(\pro... ...q}\frac{(2n-D_1)}{(2n+D_2)}\right)\frac{2(1+q)-D_1}{2} L^{-q}.$$ (49)

This is also the relative error in $\log(p)$ since it is proportional to $I_{m,n}$. In practice, unlike the T score approximation the error improves with increased iterations and is well within the required error with 20 iterations for $F > 1$ and for any degrees of freedom.