Fourth Order extension

In the fourth order case, the expressions for $\frac{h_\theta(\theta)}{h(\theta)}$, $\frac{f_\theta(m\vert\theta)}{f(m\vert\theta)}$, $F_\theta(\theta)$ and $G_\theta(\theta)$ have to be derived. Then, a fourth-order estimate $\hat{\theta}$ can be found by substituting the results into equation ().

$$\begin{split} \frac{h_\theta(\theta)}{h(\theta)} &= 0 \\ \f... ...= - \frac{18N}{\theta^4} + \frac{18N}{(1-\theta)^4} \end{split}$$ (55)

Although equation () cannot be solved analytically for $\theta$, it can still be solved numerically.