Let's say, for instance, you have normally distributed data that is coming in one at a time. At some unknown instance, the distribution parameters (mean and variance) change. Assuming that there is not infinite memory, what would be the best way to determine how many samples are need to estimate the new distribution?
In this case, I was trying to play with a toy example where the first 100 events are drawn from N(100,20) and then at some unknown time, events are drawn from N(120,5). Intuitively, I think that it would take much longer to realize the variance shift in the distribution (i.e. it would take longer to detect a change moving from a very wide distribution to a narrow distribution, vs it would quickly be detected if you had a very narrow distribution previously and then shifted to a large distribution), but I'm not sure what the proper way to show this would be.
Any advice is greatly appreciated. Thanks!
Edit: Also in this case, the mean and variance of both the pre and post break point are unknown. Thanks