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Let's assume we have a forest.

And there is a breed of rabbits that is visiting that forest all the time.

It is possible to distinguish every individual rabbit.

There are devices in that forest that count the visits of every individual rabbit on a daily basis; so there are not two or more visits for a specific rabbit on one day; a rabbit stay the whole day so to say.

The information I have is e.g.:

  • rabbit #343 visited the forest on May 5th 2012 for the 12th time.
  • rabbit #793 visited the forest on June 2nd 2012 for the 1st time.

now the CEO of the forest wants to measure if there is a tendency of rabbits not coming back.

and I am the CEO's data guy and have to figure that out.

My question is if this "problem type" is known under a specific label - I guess it is - and if there is something like an established formula to indicate the "back out rate" or the "loyalty rate" / "probability of another visit extrapolated for all rabbits".

What I will do is to chart for multi-day-time-periods (e.g. a week)

  • the number of rabbits that visited for the first time
  • and the number of rabbits that visited for the last time (e.g. hindsight knowledge for six month)

but I doubt that is the most efficient way to go about this question.

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    $\begingroup$ In a business-analytic context, this is often referred to as churn modeling or churn prediction. It employs a wide variety of statistical ideas and methodologies including survival analysis, Markov-chain and stochastic-process theory, hierarchical Bayes models, etc. $\endgroup$ – cardinal Jul 13 '12 at 12:53
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    $\begingroup$ my stochastic knowlege got through time a tad rusty ... what would be a solid yet simple algorithmic approach. but thanks for the labelling. if you put it more verbose with a useful link for further reading, I could accept it as an answer. $\endgroup$ – Raffael Jul 13 '12 at 18:45
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    $\begingroup$ Can you give some more examples of how you would want to use the data? Decisions it might be applied to, etc. "Measure if there is a tendency of rabbits not coming back" is very broad. A more specific example could be "Evaluate the success of an email followup campaign by dividing new rabbits into two experimental groups with and without the campaign and calculating the % that return at least once after their first visit." $\endgroup$ – Jonathan Jul 13 '12 at 20:06
  • $\begingroup$ Although, if all you need is the name I guess that's not necessary. $\endgroup$ – Jonathan Jul 13 '12 at 20:07
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In a business-analytic context, this is often referred to as churn modeling or churn prediction. It employs a wide variety of statistical ideas and methodologies including survival analysis, Markov-chain and stochastic-process theory, hierarchical Bayes models, etc.

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  • $\begingroup$ I've copied this comment by @cardinal as a community wiki answer because the comment is, more or less, an answer to this question. We have a dramatic gap between answers and questions. At least part of the problem is that some questions are answered in comments: if comments which answered the question were answers instead, we would have fewer unanswered questions. $\endgroup$ – mkt - Reinstate Monica Jun 19 at 6:46

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