As the title says, I am interested in computing or approximating a percentile (e.g. 95%) for a large time interval (e.g., 1h) based on the percentiles of smaller time windows (30s). I am aware that the correct way would be to compute the percentile from scratch starting from the raw data. However, the data set is very large and would take way too much time (a 30s window can have 100k-100M data points).
To simplify things, assume that the distribution for all the time intervals are the same but the constants might be somewhat different. For example, values in a window follow a Poisson distribution but the parameters of the distribution might vary somewhat between windows. To put it in more visual terms, the shape of all the distributions is the same but there might be a "scaling" factor that changes.
I do not require a mathematical proof but some insight on what would be a reasonable way to proceed. Right now I am computing the median value of all the percentiles I am interested in. Could I improve on this?