Gamma Distribution

Position of rthr^{th} random point.

f(x)=λrΓ(r)xr1eλx1[0,)(x)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 λ\lambda.

We have

FNB(r,p)FΓ(r,p)rp1p\left\|F_{N B(r, p)}-F_{\Gamma(r, p)}\right\|_{\infty} \leq r \frac{p}{1-p}