Probability of period without event I have a data set of a list of invoices each of which have a date.  I'm trying to detect when I might consider that a customer has stopped ordering a part.
The way I'm approaching this might be completely wrong.  I'm taking the invoices, ordering by date, and then counting the difference between dates of consecutive invoices.  I then produce a nice graph and it lets me say something like "95% of all orders were within 15 days of each other".  I don't know where to go next :)  Is this concept at all related to the Pareto distribution?
Reading up on the Poisson distribution I can take the same data and produce the probability of N invoices per day.  I get something like 57% of days have 0 invoices, 23% have 1 invoice, 12% have 2 invoices, etc.  At this point I get to the not knowing what I'm doing part :)
The end goal is to be able to notice stopped orders, ideally with some kind of tweakable 'confidence' cutoff.  I'm afraid of using the 'confidence' word because I assume to be using it wrong.
Thanks!
 A: Refer to the following paper:
Schmittlein, D.C. and Morrison, D.G. (1985), “Is the customer still active?”, The American. Statistician, Vol. 39, pp. 291-5.
Quote from this paper: 

Letting the observation period be one unit of time and assuming
  Poisson-process purchasing during the customer's active phase, the
  number of purchases $n$ and the time of the last purchase $t$ contain
  all of the information. The $p$ level for testing the hypothesis that
  the customer is still active at the end of the observation period is
  found to be simply $t^n$.

The authors give several examples, such as a case in which $n=4$ purchases are made during the observation period, with the last purchase made $9/10$ of the way to the end of the observation period. So the $p$ level is $(0.9)^4=0.66$, which is not less than 0.05, so the customer is still active.
A: Well,
the first problem here is that IMHO yours are not useful statistical variables as they are now.
Consider that orders of a part by a customer (I'm guessing here about your business segment, bear with me) are driven by many correlated variables like:


*

*Seasonality

*Customer needs of that part

*Market situation


and so on...
In this case many times you first apply different algorithms to make this "noise" disappear , but even in this case what you could assume through a poisson distribution greatly depends on how that distribution fits with your data.
My two cents here: cluster customers depending on orders history (frequency, amount and so on) and next think about the aggregate demand of that part, which is more easily analysed thought standard models.
