Alternative Equation Formats

The equation on this page is available in multiple formats. Depending on your browser, some formats might not render correctly.

MathML

\begin{array}{rcl} f (y) & = & {\begin{cases} ω + (1 - ω) (1 + k λ)^{- \frac{1}{k}} for y = 0 \\ (1 - ω) \frac{Γ (y + 1 / k)}{Γ (y + 1) Γ (1 / k)} \frac{(k λ)^{y}}{(1 + k λ)^{y + 1 / k}} for y = 1, 2, \dots \end{cases} \\ ϕ & = & 1 \\ d i s p e r s i o n & = & k \\ μ = E (Y) & = & (1 - ω) λ \\ V a r (Y) & = & (1 - ω) λ (1 + ω λ + k λ) \\ = & μ + (\frac{ω}{1 - ω} + \frac{k}{1 - ω}) μ^{2} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} f(y) & = & \left\{ \begin{array}{l} \omega + (1-\omega )(1+k\lambda )^{-\frac{1}{k}}~ ~ ~ \mbox{for } y=0 \\ (1-\omega ) \frac{\Gamma (y+1/k)}{\Gamma (y+1)\Gamma (1/k)} \frac{(k\lambda )^ y}{(1+k\lambda )^{y+1/k}} ~ ~ ~ \mbox{for } y = 1,2,\ldots \\ \end{array} \right. \\ \phi & = & 1 \\ \mr{dispersion} & = & k \\ \mu = \mr{E}(Y) & = & (1-\omega )\lambda \\ \mr{Var}(Y) & = & (1-\omega )\lambda (1+\omega \lambda + k\lambda ) \\ & = & \mu + \left(\frac{\omega }{1-\omega }+\frac{k}{1-\omega }\right)\mu ^2 \\ \end{eqnarray*}