Alternative Equation Formats

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MathML

\begin{array}{rcl} \hat{V} ({\hat{F}}_{D} ({\hat{Q}}_{D} (p))) & = & \sum_{h = 1}^{H} \frac{n_{h} (1 - f_{h})}{n_{h} - 1} \sum_{i = 1}^{n_{h}} (e_{h i \cdot} - {\bar{e}}_{h \cdot \cdot})^{2} \\ e_{h i j} & = & I_{D} (h, i, j) (I (y_{h i j} \leq {\hat{Q}}_{D} (p)) - {\hat{F}}_{D} ({\hat{Q}}_{D} (p))) - {\hat{θ}}_{D}^{(r)} ({\hat{Q}}_{D} (p)) \\ - (I_{D} (h, i, j) - {\hat{\bar{I}}}_{D}^{(r)}) {\hat{θ}}_{D} (p) \\ e_{h i \cdot} & = & \sum_{j = 1}^{m_{h i}} {\tilde{w}}_{h i j} e_{h i j} / {\tilde{w}}_{\cdot \cdot \cdot} \\ {\bar{e}}_{h \cdot \cdot} & = & (\sum_{i = 1}^{n_{h}} e_{h i \cdot}) / n_{h} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} \hat V(\hat F_ D(\hat Q_ D(p))) & =& \sum _{h=1}^ H \frac{n_ h(1-f_ h)}{n_ h-1} ~ \sum _{i=1}^{n_ h} {(e_{hi\cdot }-\bar{e}_{h\cdot \cdot })^2} \\ e_{hij} & =& I_ D(h,i,j) \left( I(y_{hij} \le \hat Q_ D(p)) - \hat F_ D(\hat Q_ D(p))\right) ~ -~ {\hat{\theta }}^{(r)}_ D(\hat Q_ D(p)) \\ & & ~ -~ \left( ~ I_ D(h,i,j) ~ -~ {\hat{\bar{I}}}_{D}^{(r)} ~ \right) ~ \hat\theta _ D(p) \\ e_{hi\cdot }& =& \sum _{j=1}^{m_{hi}}~ \tilde{w}_{hij} e_{hij} /\tilde{w}_{\cdot \cdot \cdot } \\ \bar{e}_{h\cdot \cdot } & =& \left( \sum _{i=1}^{n_ h}e_{hi\cdot } \right) / ~ n_ h \end{eqnarray*}