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Imagine new product hitting the market, sales dynamically rise, achieve plateau, and then steadily drop. I'm thinking of something with dynamics that when depicted on a plot (counts over time), will resemble Little Prince's drawing of snake who ate an elephant (well, maybe with less extreme drop at the end).

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What would be the best model for such process? I imagine I could find some interesting hints in epidemiological models -- if yes, could you suggest something? I'm looking for something relatively simple, using just counts over time as data.

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  • $\begingroup$ Something simple would be like a polynomial (Koyck or Almon) distributed lag model with a dead start effect. $\endgroup$ – Graeme Walsh Sep 29 '16 at 20:40
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    $\begingroup$ The textbook is the [Bass sales diffusion model. ](faculty.biu.ac.il/~fruchtg/829/lec/6.pdf). Variations on mixtures are used by big folks in order to have multiple sequential new products - to truncate sales of last years cars and improve sales of this years cars. $\endgroup$ – EngrStudent Sep 30 '16 at 11:28

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