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Sorry for the self-referential title ;)

I'd be curious to know what's a curve that could be used to model - in the scale of (say) weeks* - the "engagement lifecycle" of a single news page of an online newspaper in terms of webpage views. The same model could be applied for Stack Exchange questions views too!

What I would intuitively model is the initial spike of visits due to the fact that a new, fresh page is very visible as it's linked in the homepage (triggering also social media reshares) and then the long-term visit behavior e.g. due to that page being reached from links from other webpages, or via search engines.

One possible way would then be the sum of two Poisson processes (the first switching off after some typical characteristic time).

Another possibility would be using something like exponential decay to capture a decay over time of interest (the "freshness" of the content fades, and so does public interest).

Is anyone aware of better alternatives or literature on this?

*I wouldn't model day-night nor weekly seasonality.

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    $\begingroup$ I am curious too for a technical discussion of this, though having seen data organically my sense is that there is no one model, virality and mid/long tail and authority and value and so forth produce many different shapes. $\endgroup$ – Jonah Benton Aug 5 '18 at 15:32
  • $\begingroup$ what about a log-normal distribution to capture the initial spike of interest? $\endgroup$ – Zeus May 11 '19 at 7:56
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One way too look at this problem, by looking at the literature, seems to frame it as an Hawkes process, as e.g. in Rizoiu et al., https://arxiv.org/abs/1602.06033 .

The paper also cites previous work using other modeling approaches: One set of approaches describe popularity dynamics [...] as being power-law shapes from either an exogenous shock or endogenous relaxation, a combination of power-law and exponential decay, multiple power-law decays with periodicity or a collection of recurrence peaks.

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The first step would be to get data. stack overflow allow for a lot of requests over here : https://data.stackexchange.com/stackoverflow/queries, but I don't know if you would be able to get a lot of time series / if those time series would be granular enough.

The second one would be to build a model (look at Davide Fiocco answer). But I am afraid that you would have to make some assumptions, like your post views dynamics being similar to other average Data.SE post, when your question is in fact a cool meta-question.

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