I know that the sum of $k$ independent exponentially distributed random variables each with density function: $$\displaystyle \lambda\,{{\rm e}^{-\lambda\,x}}$$ has an Erlang distribution: $$\displaystyle {\frac {{\lambda}^{k}{x}^{k-1}{{\rm e}^{-\lambda\,x}}}{ \left( k-1 \right) !}} $$ What would the sum density function look like for a sum of k independent exponentially distributed random variables, each with a density function: $$\displaystyle \lambda\,{{\rm e}^{-\lambda\,(x-a)}},$$ where $a$ is a shift parameter.