Are random variables for a Weibull distribution additive?

Let's say there are random variables $\displaystyle X$ and $\displaystyle Y$ with different Weibull distributions. The Weibulls are very similar, but not one and the same as both parameters vary slightly.

How would the distribution of $\displaystyle Z = X + Y$ look like? Would it be Weibull, and if so, what are the parameters?