Computing probability theory: what is ξ(ω) + η(ω), at least approximately?

There are several distributions: gamma, lognormal, and even such that with probability p we have some "normal" distribution, and with probability 1−p is zero.
There are two random variables — we believe that independent. An approximation to the distribution function of the sum ξ(ω) + η(ω)?
July 2nd 19 at 17:50
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