Alternative Equation Formats

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MathML

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

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Math as LaTeX Source

\begin{eqnarray*} U^{(1)}_ k(t) & =& \left( \sum _{j=1}^ n \mr{e}^{\bbeta '\bxi _{j}} \hat{S}_ k(t,\bxi _{j}) \right)^2 \sum _{t_ i\leq t} \frac{d(t_ i)}{[S^{(0)}(\hat{\bbeta },t_ i)]^2}, \quad k=1,2 \\ U^{(2)}_{12}(t)& =& \left\{ \sum _{j=1}^ n \left[\hat{S}_1(t,\bxi _{j})H_1(t,\bxi _{j})-\hat{S}_2(t,\bxi _{j})H_2(t,\bxi _{j}) \right] \right\} ^{\prime } \mc{I} ^{-1}(\hat{\bbeta }) \\ & & \left\{ \sum _{j=1}^ n \left[\hat{S}_1(t,\bxi _{j})H_2(t,\bxi _{j})-\hat{S}_1(t,\bxi _{j})H(_2t,\bxi _{j}) \right] \right\} \end{eqnarray*}