bound of Erlang distribution Is there any known polynomial bound of the Erlang distribution? I'd like to say that, given $k$ and $\lambda$ with probability p the r.v. is going to be less than some value x.

That is simply the cumulative distribution function, given in WP by $\gamma(k,k\lambda)/(k-1)! = 1-\sum_{n=0}^{k-1}\mathrm e^{-\lambda x}(\lambda x)^{n}/n! $, where $\gamma$ is the incomplete gamma function.
