A few months ago, I wrote an Android App. I am getting two key pieces of data from this app regarding its usage. The first metric, is number of downloads per day. The second metric, is basically, how many times the app is used in that day. Obviously there is a correlation. If I get 25 downloads in a day, there are more uses that day, than if there are only 5 downloads that day. I am wondering how I can attack the problem of determining how many of the 'uses' are due to recurring users, and how many of the uses are due to new users. Any ideas or criticisms are appreciated! I do have a background (from school long ago) in Calc as well as basic statistics.
You didn't provide many information and data exampe so I will make a few assumptions on the go. I assume new uses are app uses in the first day of the first launch of downloaded app. Recurrent uses are made by users who launched the app in more than one separate day. I assume you have data on uses and downloads per day. Let's assume that if you download app you will use it the same day (reasonable assumption).
So lets say $d_i$ denote downloads at day $i$ and $u_i$ denote uses at day $i$.
$u_1/d_1=R_1$ gives you the ratio of uses per download on the first day. You can use this ratio to estimate how many times new users use the application. Then with $d_2 R$ you get number of uses from new users on the second day and with $u_2-d_2R$ you get the number of uses from the users downloading the previous day - recurrent users. Number of recurrent uses on day $i$ is thus:
And number of uses from new uses is simply:
With this method you can also calculate the number of uses made by users who are one day old to $i$ days old with $i$ denoting the current date. So this gives you information about use dependent on the time since download. That can be very useful. But since you didn't ask about that I will show it only if you are interested.