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

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SUMMARY

The discussion focuses on calculating long-term probabilities using probability density functions (PDFs), specifically in the context of a log-normal distribution. The user seeks to understand how to account for time when assessing the probability of an event occurring over extended periods, such as 30 years. Key suggestions include modeling distribution parameters as functions of time and utilizing the Fokker-Planck equation to address changes in distribution shape over time. The concept of a metadistribution, defined as H(x) = w F(x) + (1-w) G(x), is also introduced as a potential solution.

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  • Understanding of probability density functions (PDFs)
  • Familiarity with log-normal distribution characteristics
  • Knowledge of the Fokker-Planck equation
  • Concept of metadistributions in probability theory
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  • Research the application of the Fokker-Planck equation in probability modeling
  • Explore methods for parameterizing distributions as functions of time
  • Study the concept of metadistributions and their practical applications
  • Investigate long-term forecasting techniques in statistical analysis
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Statisticians, data scientists, and researchers involved in long-term probability modeling and forecasting, particularly those working with log-normal distributions and advanced probability theories.

Drewau2005
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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
 
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You could model the parameters of your distribution to be simple functions of time.
 
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.
 

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