I have encountered this problem on how to predict the probability of a periodically happening event occurring at a given time.
For example, we have an event called being_an_undergrad. There are many data points: bob is an undergrad from (1999 - 2003), Bill is an undergrad from (1900 - 1903), Alice is an undergrad from (1900 - 1905), and there are many other data points such as (2010 - 2015), (2011 - 2013) ....
There are many events(data points) of being_an_undergrad. The lasting interval varies, it might be 1 year, 2 years, 3 years, .... or even 10 years. But the majority is around 4 years.
However, I am wondering given all the data points above. If I now know that Jason starts college in 2021, and how can I calculate/predict the probability that he will still be an undergrad in 2022? and 2023? and 2024 .... 2028, etc.
My current dataset consists of 10000 tuples representing events of different relations. The relations are all continuous relations similar to the example above. There are about 10 continuous relations in total in this dataset, such as
livesIn, etc. For each relation, there are about 1000 data points(1000 durations) about this relation, for example,
<Leo, isUndergrad, Harvard, 2010 - 2011>, <Leo, isUndergrad, Stanford, 2013 - 2016>..... <Jason, livesIn, US, 1990 - 2021>, <Richard, livesIn, UK, 1899- 1995> ...
My problem now is that I want to get a confidence level(probability) when I want to predict one event happening at a specific time point. For example, I want to predict the probability that event <Jason, livesIn, US, 2068> happens, given:
1.the above datasets which includes info about the relation:
2.the starting time when Mike lives in US, say he started to live in US since 2030.
I have used normal distribution to simulate, but I am wondering if there are any other better AI / ML / Stats approaches. Thanks a lot!