I want to find out whether there is a concise expression (i.e. not a convolution) for the distribution of a random variable A which is the sum of $n$ i.i.d. rv's $B_i$, which are themselves double exponentially distributed with density $f_B(x) = 1_{x>0} \, p \, \eta^+ e^{-\eta^+ x} + 1_{x<0} \, q \, \eta^- e^{\eta^- x}$ , where $p+q = 1, p \ge 0, q \ge 0, \eta^+ > 0, \eta^- > 0$.
One route of thought went the way from the distribution of a sum of exponential rv's $C_i$ (with density $f_C(x) = 1_{x>0} \, \eta \, e^{-\eta x}, \, \eta > 0$) being a gamma distribution; so - is there anything similar?