Let's assume I have 1 year of weekly sale data for software A and 1 year of weekly sale data for software B.
Software B is related to software A, because it's a maintenance/security upgrade, so the customer can only purchase B once they purchased A, (but they don't have to, i.e. computer got broken)
There is no relational data between each sale of B for each sale of A.
Assume I sell software A, 50000 products /year, but I don't have any data to whom I sell it to. Would it be possible to somehow find how many product B sales are expected for every product?
More importantly, does this have anything to do with a Poisson process, since I already have the data? Wouldn't it be just a simple linear relationship?
I think you come up with a probability that a customer that bought software A buys software B.
Each weekly figure is an observation $(a_n, b_n)$ of sales of each type. $T_n$ is the total number of sales in that week. $B_n \sim binomial(t_n,p)$. Here we are just saying that the weekly sales of software B are given by a binomial distribution with trials = total number of sales.
$p$ is modelled by a maximum likelihood estimate of getting $b_n$ sales in week $n$ given that $s_n = \sum_{k<n} a_k-b_k$ of software A was sold so far (take away total number of software B sold so far) so $s_n$ is the number of potential customers for software B in week $n$.
I.e. we maximise the following likelihood of our data $b_n$
$L(p|\textbf{b}) = \prod_{n=1}^{N} binp(b_n; s_n,p)$
We assume that $p$ is only related to total number of software A sold so far.
This model assumes that the chance of any given sale of product B is dependent only on the number of product A sold so far, and doesn't (yet!) take into market factors.