
\subsection{\bf 5.3\hspace{1em} Bartlett's Function---Overview}
\begin{slide}
\begin{itemize}

\item The previous analysis can be generalized to Bartlett's $S$
function which is defined as
\[
S(\lambda ) = \frac{1}{\sqrt{I(\lambda)}}\ \frac{\partial\ln L}{\partial\lambda}
\]

\item $I(\lambda )$ is the information $\left\langle \left(
\frac{\partial}{\partial\lambda} \ln L \right)^2 \right\rangle$
\[
I(\lambda) = N \int\limits \left\lbrack \frac{\partial}{\partial\lambda} \ln
P(x, \lambda) \right\rbrack^2 P(x, \lambda ) dx
\]

\item where $N$ = Number of events and ${\displaystyle\int\limits} \left\lbrack 
\frac{\partial}{\partial\lambda} \ln P (x,\lambda) \right\rbrack^2
P(x,\lambda) dx$ can be calculated from theoretical forms.
\end{itemize}
\end{slide}

