Gamma density
= Gamma density
{title2=$f(y)=\theta^k y^{k-1}e^{-\theta y}/\Gamma(k),\quad y>0$}
The <probability density function> of a <Gamma distribution> with shape $k>0$ and rate $\theta>0$. Integration against $y^{-j}$ gives $\mathbb E[Y^{-j}]=\theta^j\Gamma(k-j)/\Gamma(k)$ when $j<k$; the integral diverges for $j\geq k$. Rate and scale are reciprocal conventions and must be distinguished.