What is the best approach for calculating long-term probability using a PDF?

[Drewau2005]

Hi

I posted the other day but I think I could have explained better what I am looking for, so hence this post.

I was wondering how you account for time when using a PDF to try and ascertain the probability of an event happening over very long periods of time?
If I have a data series which is described by a distribution, say log-normal and I want to work out the proabability of x being greater than y happening say by 30 years ? I guess it is allied to asking to what happens if you are using the area under the curve to look at probabilities when the distribution might change shape substantially over a long sweep of time and could be better described by a different equation.

Would you use the Fokker-Planck equation in this instance ?

Many thanks
D

 

[EnumaElish]

You could model the parameters of your distribution to be simple functions of time.

 

[EnumaElish]

Or, you could define a metadistribution H(x) = w F(x) + (1-w) G(x) where 0 < w < 1 is a monotonic function of time.