mixing distributions

Hallo,

the problem is as follows:

I have a dataset and want to fit a distribution on it. I found that in the
left area e.g. a lognormal distribution fits very well and in the right area
the pareto distr fits very well. First I tried to put them together via
"splicing". That means, the compound distr is a defined as lognormal below
x=u and as pareto else.
But the problem with this approach is that I have to chose a single u, whats
sometimes quiet difficult.
So I think of a modification ... why setting u as fixum instead of taking a
mixing of the both functions?

The Idea is: I sum up the two distributions with a variable weighting so the
lognormal dominates in the leftern and the pareto in the rightern part of
the compound distr. The weighting should be another function (e.g. the
normal CDF)
Sadly my first tries with such a mixing criterion didnt work. I found that
with such a mixing the result is not a density function because:

* the CDF is not monotonic increasing if I use the CDF
* the mass under the curve is <> 1 if I use the density functions

So ... what now? Does anybody know a solution for the setting above?

Thank you very much for any reply.


.

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