Gamma Distribution

Position of $r^{th}$ random point.

$f(x)=\frac{{\lambda }^r}{\Gamma (r)}{x}^{r-1}{e}^{-\lambda x}{1}_{[0,\infty )}(x)$ Gamma Function

r-fold sum of independent Exponential Distributions with parameter $\lambda$.

We have

$${\Vert F_{NB(r,p)}-F_{\Gamma (r,p)}\Vert }_{\infty }\le r\frac{p}{1-p}$$