Alternative Equation Formats

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MathML

\begin{array}{rcl} S^{(0)} (β, k, t) & = & \sum_{i} Y_{i} (t) {1 - \frac{k - 1}{d (t)} Δ_{i} (t)} e^{β^{'} Z_{i} (t)} \\ S^{(1)} (β, k, t) & = & \sum_{i} Y_{i} (t) {1 - \frac{k - 1}{d (t)} Δ_{i} (t)} e^{β^{'} Z_{i} (t)} Z_{i} (t) \\ \bar{Z} (β, k, t) & = & \frac{S^{(1)} (β, k, t)}{S^{(0)} (β, k, t)} \\ d Λ_{0} (β, k, t) & = & \sum_{i} \frac{d N_{i} (t)}{S^{(0)} (β, k, t)} \\ d M_{i} (β, k, t) & = & d N_{i} (t) - Y_{i} (t) (1 - Δ_{i} (t) \frac{k - 1}{d (t)}) e^{β^{'} Z_{i} (t)} d Λ_{0} (β, k, t) \end{array}

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Math as LaTeX Source

\begin{eqnarray*} S^{(0)}(\bbeta ,k, t) & =& \sum _{i} Y_{i}(t) \biggl \{ 1- \frac{k-1}{d(t)} \Delta _{i}(t) \biggr \} \mr{e}^{\bbeta '\bZ _{i}(t)} \\ S^{(1)}(\bbeta ,k,t) & =& \sum _{i} Y_{i}(t) \biggl \{ 1- \frac{k-1}{d(t)} \Delta _{i}(t) \biggr \} \mr{e}^{\bbeta '\bZ _{i}(t)} \bZ _{i}(t) \\ \bar{\bZ }(\bbeta ,k,t) & =& \frac{ S^{(1)}(\bbeta ,k,t)}{ S^{(0)}(\bbeta ,k,t) } \\ d\Lambda _0(\bbeta ,k,t) & = & \sum _ i\frac{dN_ i(t)}{S^{(0)}(\bbeta ,k,t)} \\ dM_ i(\bbeta ,k,t) & = & dN_ i(t) - Y_ i(t)\biggl ( 1- \Delta _ i(t) \frac{k-1}{d(t)} \biggr ) \mr{e}^{\bbeta '\bZ _ i(t)} d\Lambda _0(\bbeta ,k,t) \end{eqnarray*}