Alternative Equation Formats

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MathML

\begin{aligned} ϕ & = (1 - ρ^{2}) / ρ^{2} \\ l (μ_{i}, ρ; y_{i}) & = \log {Γ (n_{i} + 1)} - \log {Γ (y_{i} + 1)} \\ - \log {Γ (n_{i} - y_{i} + 1)} \\ + \log {Γ (ϕ)} - \log {Γ (n_{i} + ϕ)} + \log {Γ (y_{i} + ϕ μ_{i})} \\ + \log {Γ (n_{i} - y_{i} + ϕ (1 - μ_{i}))} - \log {Γ (ϕ μ_{i})} \\ - \log {Γ (ϕ (1 - μ_{i}))} \\ l (μ_{i}, ρ; y_{i}, w_{i}) & = w_{i} l (μ_{i}, ρ; y_{i}) \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} \phi & = (1-\rho ^2)/\rho ^2 \\ l(\mu _ i,\rho ; y_ i) & = \log \{ \Gamma (n_ i+1)\} - \log \{ \Gamma (y_ i+1)\} \\ & - \log \{ \Gamma (n_ i-y_ i+1)\} \\ & + \log \{ \Gamma (\phi )\} - \log \{ \Gamma (n_ i+\phi )\} + \log \{ \Gamma (y_ i+\phi \mu _ i)\} \\ & + \log \{ \Gamma (n_ i-y_ i + \phi (1-\mu _ i))\} - \log \{ \Gamma (\phi \mu _ i)\} \\ & - \log \{ \Gamma (\phi (1-\mu _ i))\} \\ l(\mu _ i,\rho ; y_ i,w_ i) & = w_ i l(\mu _ i,\rho ; y_ i) \end{align*}