How to collect the mobile app data using AWS service(s) or other solutions?

I would like to build an app and collect some events from the app, and then show some event statistics like frequency, duration etc.

I`ve just investigated the aws Cognito web service, but it stores only a set of key-value pairs of a limited total size.

I can build, of course, my own REST web service on the top of the database and store all my events there. But I wonder if there are some aws web service(s) that I can leverage to build such a solution. (In case if someone familiar with Azure, it would be nice to see the possible solution there too!)

Any ideas, suggestions?