Alternative Equation Formats

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MathML

\begin{array}{rcl} S_{l}^{(0)} (β_{l}, k, t) & = & \sum_{i} Y_{i} (t) {1 - \frac{k - 1}{d (t)} Δ_{i} (t)} \exp (β_{l}^{'} Z_{i}) \\ S_{l}^{(1)} (β_{l}, k, t) & = & \sum_{i} Y_{i} (t) {1 - \frac{k - 1}{d (t)} Δ_{i} (t)} \exp (β_{l}^{'} Z_{i}) Z_{i} \\ {\bar{Z}}_{l} (β_{l}, k, t) & = & \frac{S_{l}^{(1)} (β_{l}, k, t)}{S_{l}^{(0)} (β_{l}, k, t)} \\ W_{l} (t) & = & \exp (β_{l}^{'} z_{0}) \sum_{i} \int_{0}^{t} \frac{1}{d (s)} \sum_{k = 1}^{d (s)} Y_{i} (s) (z_{0} - {\bar{Z}}_{l} (β_{l}, k, s)) \frac{d N_{i}^{l} (s)}{S_{l}^{(0)} (β_{l}, k, s)} \end{array}

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Math as LaTeX Source

\begin{eqnarray*} S^{(0)}_ l(\bbeta _ l,k,t) & =& \sum _{i} Y_{i}(t) \biggl \{ 1- \frac{k-1}{d(t)} \Delta _{i}(t) \biggr \} \exp (\bbeta _ l'\bZ _{i}) \\ \bS ^{(1)}_ l(\bbeta _ l,k,t) & =& \sum _{i} Y_{i}(t) \biggl \{ 1- \frac{k-1}{d(t)} \Delta _{i}(t) \biggr \} \exp (\bbeta _ l'\bZ _{i}) \bZ _{i} \\ \bar{\bZ }_ l(\bbeta _ l,k,t) & =& \frac{ S^{(1)}_ l(\bbeta _ l,k,t)}{ S^{(0)}_ l(\bbeta _ l,k,t)} \\ \bW _ l(t) & =& \exp (\bbeta _ l'\mb{z}_0) \sum _ i \int _0^ t \frac{1}{d(s)} \sum _{k=1}^{d(s)} Y_{i}(s) (\mb{z}_0 - \bar{\bZ }_ l(\bbeta _ l,k,s)) \frac{dN_ i^ l(s)}{S^{(0)}_ l(\bbeta _ l,k,s)} \end{eqnarray*}