Alternative Equation Formats

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MathML

\begin{array}{rcl} V_{12}^{(1)} (t) & = & {\sum_{j = 1}^{n} [e^{β^{'} ξ_{1 j}} \hat{S} (t, ξ_{1 j}) - e^{β^{'} ξ_{2 j}} \hat{S} (t, ξ_{2 j})]}^{2} \sum_{t_{i} \leq t} \frac{d (t_{i})}{[S^{(0)} (\hat{β}, t_{i})]^{2}} \\ V_{12}^{(2)} (t) & = & {\sum_{j = 1}^{n} [\hat{S} (t, ξ_{1 j}) H (t, ξ_{1 j}) - \hat{S} (t, ξ_{2 j}) H (t, ξ_{2 j})]}^{'} I^{- 1} (\hat{β}) \\ {\sum_{j = 1}^{n} [\hat{S} (t, ξ_{1 j}) H (t, ξ_{1 j}) - \hat{S} (t, ξ_{2 j}) H (t, ξ_{2 j})]} \end{array}

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Math as LaTeX Source

\begin{eqnarray*} V^{(1)}_{12}(t) & =& \left\{ \sum _{j=1}^ n \left[\mr{e}^{\bbeta '\bxi _{1j}} \hat{S}(t,\bxi _{1j}) - \mr{e}^{\bbeta '\bxi _{2j}} \hat{S}(t,\bxi _{2j}) \right] \right\} ^2 \sum _{t_ i\leq t} \frac{d(t_ i)}{[S^{(0)}(\hat{\bbeta },t_ i)]^2} \\ V^{(2)}_{12}(t)& =& \left\{ \sum _{j=1}^ n \left[\hat{S}(t,\bxi _{1j})H(t,\bxi _{1j})-\hat{S}(t,\bxi _{2j})H(t,\bxi _{2j}) \right] \right\} ^{\prime } \mc{I} ^{-1}(\hat{\bbeta })\\ & & \left\{ \sum _{j=1}^ n \left[\hat{S}(t,\bxi _{1j})H(t,\bxi _{1j})-\hat{S}(t,\bxi _{2j})H(t,\bxi _{2j}) \right] \right\} \end{eqnarray*}