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I am working on calculating the lifetime value of a group of individuals who registered to a site.

I am determining the lifetime value of signup and not necessarily a customer.

I am calculating lifetime value as a cumulative sum of the value of a signup on an interval of a day. For each customer, I calculate how much they spend on each day relative to the day that they signed up. So a customer who spends $10 on their day of signup has a value of 10 on day 0.

For each day I aggregate all of these values to determine the lifetime value of a group.

Day 0 LTV: Sum of all spend on the first day of signup across all customers / No. of signups

Day 1 LTV: Day 0 LTV + ( Sum of all spend on the second day of signups / No. of customers signed up for at least two days)

...etc.

Now, for Day N, as N -> infinity, the number of customers who are signed up at this point tends to 0. So my confidence in the calculation for latter days is much lower than it is for earlier ones.

How can I incorporate this lack of confidence into my calculation for lifetime value? Or should I just not calculate the lifetime value beyond a point where I have, say, less than 30 available signups?

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