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<h3>Functional relationships for <script type="math/tex">\;X \sim GAM(\kappa,\theta),\;\;X \in [0,\infty),\;\;\; \kappa,\theta\; > 0</script>
</h3>
$$
\begin{aligned}
f(x|\kappa,\theta)&=\frac{1}{\Gamma\left(\kappa\right)\theta^{\kappa}}x^{\kappa-1}e^{-x/\theta}\\\\\\\\
F(x|\kappa,\theta)&=\frac{\Gamma\left(\kappa,x/\theta\right)}{\Gamma\left(\kappa\right)}\\\\\\\\
h(x|\kappa,\theta)&=\frac{x^{\kappa-1}e^{-x/\theta}}{\left(\Gamma\left(\kappa\right)-\Gamma\left(\kappa,x/\theta\right)\right)\theta^{\kappa}\Gamma\left(\kappa\right)}\\\\\\\\\
E[X]&=\kappa\theta\\\\\\\\
Var[X]&=\kappa\theta^{2}
\end{aligned}
$$
