Asymetric double exponential distribution $X \sim AL(p,\theta_1, \theta_2)$ has the following form of density function: $$ f(x) = p \theta_1 e^{−\theta_1x} \mathbb{1}_{x<0} + (1 − p) \theta_2 e^{\theta_2x} \mathbb{1}_{x\geq0} $$ I know the Inverse CDF method of simulation random variable, but in this case I think it is not possible, because CDF can not be presented in one simple form, so my question is:
How can I simulate this distribution?