Suppose I have nonidentical exponentially distributed random variables $X$ with a time-variant rate of $\lambda_X(t)$ and $Y$ with a time-variant rate of $\lambda_Y(t)$. What is the distribution of $Z = X + Y$? Is it a hypoexponential distribution or a gamma distribution?
Still related to the above questions, if I have $Z_1$ and $Z_2$ based on the formula we obtained above, what is the distribution of $Q = Z_1 + Z_2$?
Any references would be greatly appreciated. Thanks!