Compound Distributions?

Hello,

I want to fit some distributions on a dataset. My tests up to now resulted in something like:

Distribution A fits very well from 0 to K
Distribution B fits very well above K

In a second step I have to draw random numbers from the chosen distribution (drawing uniform distr. rn and put them into the F^-1).

Now the Problem is ... : I want to put distr A and B together.

Its not sure that K is identical to the point of intersection! So it might be that the combination of A and B is not stetic in K.

So how to draw my random numbers??? If I put e.g a 0.88 into the "common" inverse in some cases not necessarily a value results - in other cases there could result two (depending whether the intersection is left or right from K).

I think there should be something to google about, but when I search for "compound distributions" I find what I would call "mixing" (e.g. F = F_A + F_B)

Who can help?

Thanks a lot!!!
.

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