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

This allows you to model the distribution as a combination of two distributions that change over time, with the weight w indicating the proportion of each distribution at a given time point. In summary, the conversation discusses the use of a PDF to determine the probability of an event happening over a long period of time and how to account for changes in the distribution over time. The suggestion is to either model the distribution parameters as functions of time or use a combination of two distributions with a weight function.
  • #1
Drewau2005
4
0
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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  • #2
You could model the parameters of your distribution to be simple functions of time.
 
  • #3
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.
 

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

What is probability and how does it relate to time?

Probability is a measure of the likelihood of an event occurring. In the context of time, probability can be used to predict the likelihood of certain events happening at a specific time in the future.

How is probability used in scientific research involving time?

Probability is often used in scientific research to understand patterns and trends over time. It can be used to make predictions about future events or to analyze data collected over a period of time.

What is the difference between theoretical and empirical probability in relation to time?

Theoretical probability is based on mathematical calculations and assumptions, while empirical probability is based on actual observations and data. In terms of time, theoretical probability can be used to make predictions about future events, while empirical probability can be used to analyze past events.

How does the concept of time affect probability?

The concept of time is important in probability as it allows us to understand the likelihood of an event occurring at a specific moment in time. Time can also impact the probability of an event, as certain events may become more or less likely as time passes.

Can probability be used to predict the future?

While probability can be used to make predictions about future events, it is important to note that it is not a guarantee. Probability is based on past data and assumptions, and therefore cannot accurately predict the exact outcome of a future event.

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