Alternative Equation Formats

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MathML

\begin{array}{rcl} ℓ & = & \sum_{{i | z_{i} = 0}} \ln [1 - Φ (w_{i}^{'} γ)] \\ + & \sum_{{i | z_{i} = 1, y_{i} = y_{i}^{*}}} {\ln [ϕ (\frac{y_{i} - {x_{i}}^{'} β}{σ})] - \ln σ + \ln [Φ (\frac{w_{i}^{'} γ + ρ \frac{y_{i} - {x_{i}}^{'} β}{σ}}{\sqrt{1 - ρ^{2}}})]} \\ + & \sum_{{i | z_{i} = 1, y_{i} = 0}} \ln \int_{- \infty}^{\frac{- {x_{i}}^{'} β}{σ}} \int_{- {w_{i}}^{'} γ}^{\infty} ϕ_{2} (u, v, ρ) d u d v \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} \ell & =& \sum _{\{ i|z_{i}=0\} }\ln [1-\Phi (\mb{w}_{i}'\bgamma )] \\ & +& \sum _{ \{ i|z_{i}=1,y_{i}=y_{i}^{*}\} } \left\{ \ln \left[\phi (\frac{y_ i-\mb{x_ i}'\bbeta }{\sigma })\right] - \ln \sigma + \ln \left[\Phi \left(\frac{\mb{w}_{i}'\bgamma + \rho \frac{y_ i-\mb{x_ i}'\bbeta }{\sigma }}{\sqrt{1-\rho ^2}}\right)\right] \right\} \\ & +& \sum _{ \{ i|z_{i}=1,y_{i}=0\} } \ln \int _{-\infty } ^{\frac{-\mb{x_ i}'\bbeta }{\sigma }} \int _{-\mb{w_ i}'\gamma } ^{\infty } \phi _2(u,v,\rho ) \, du\, dv \end{eqnarray*}