statistics.tex

\centering
\begin{threeparttable}
\begin{tabular*}{0.47\textwidth}{@{\extracolsep{\fill}}ll}
    \toprule
	Statistic & Formula \\
	\midrule
	leastsq \rule{0pt}{3ex} & $\sigma^{2} \equiv 1$ \\
	chi2datavar\tnote{a} \rule{0pt}{3ex}  & $\sigma^{2} \equiv D_{i}$ for $D_{i} > 0$ \\
	chi2constvar \rule{0pt}{3ex} & $\sigma^{2} \equiv \dfrac{\sum_{i}^{N} D_{i}}{N}$ \\
	chi2modvar\tnote{b} \rule{0pt}{3ex} & $\sigma^{2} \equiv M_{i}$ \\
	chi2gehrels \rule{0pt}{3ex} & $\sigma^{2} \equiv \left[1 + \sqrt{D_{i} + 0.75}\right]^{2}$ \\
	chi2xspecvar \rule{0pt}{5ex} & $\sigma^{2} \equiv 
		\begin{cases}
			D_{i}, & \text{if}\ D_{i} > 0 \\
			1, & \text{if} D_{i} = 0
		\end{cases}$ \\
	cash \rule{0pt}{3ex} & $C \equiv 2 \sum_{i}[M_{i} - D_{i} \log{M_{i}}]$ \\
	cstat \rule{0pt}{4ex} & $C \equiv 2 \sum_{i}\left[M_{i} - D_{i} + 
							D_{i} \left(\dfrac{\log{D_{i}}}{\log{M_{i}}}\right)\right]$ \\
    \bottomrule
\end{tabular*}
\begin{tablenotes}
\item [a] If errors are provided, $\sigma_{i}^{2}$ is taken from these errors.
		  Else, $\sigma_{i}^{2}$ is computed from the y-values of the data points.
\end{tablenotes}
\end{threeparttable}

%\def\arraystretch{1.8} \rule{0pt}{4ex}