= Shifted gamma distribution
{title2=$V=k+Y,\quad Y\sim\operatorname{Gamma}(\alpha,\nu)$}
= Translated gamma distribution
{synonym}
A <gamma distribution> translated by a real constant $k$. With shape $\alpha>0$ and rate $\nu>0$, its support is $(k,\infty)$ and its first three <cumulants> are $k+\alpha/\nu$, $\alpha/\nu^2$, and $2\alpha/\nu^3$. Its <skewness> is $2/\sqrt\alpha$. A negative shift permits negative values; introducing a shift does not automatically respect the nonnegative support of an insurance loss.
Back to article page