Estimating the number of monthly active users in a website
I have this real-world problem that perhaps you'll be able to help me solve.
Let's say I operate a website and want to estimate the number of unique active users I'll have in a given month, by looking at the numbers for the first few days.
So on the first day of the month I count k1 unique users that used the website, and all of them are new (since I haven't seen them before this month), so the number of first-seen users is n1 so that n1=k1.
On the second day I count k2 unique users, of which there are n2 first-seen users. n2 is typically smaller than k2, since some of the users on the second day have already been counted in the first day.
And so I continue counting the number of unique users ki and the number of first-seen users ni for a few days.
No the question is, how can I estimate the total monthly unique active users given the measurements in the first i days of the month?
Re: Estimating the number of monthly active users in a website
I think you'll want to look at the progression of the proportion N = n(i)/k(i). If you can do some kind of regression on it, you can make a function N(i). I think an exponential regression might fit the bill, but I'm not quite sure.
Given the function N(i) and assuming that you have some average number of visitors A, you can sum N(i) * A to get an estimate for the total number of unique active users.
Of course, the prediction will be better if you have more data (days). Also, if your average number of visitors fluctuates wildly, the prediction won't be so great.