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Let's assume you are measuring the physical activity levels over a day of some people, using accelerometry for example. The goal is to quantify the "clumpiness" of the activity patterns. It should discriminate between people that are physically active in many shorter bouts (upper graph in the picture below) and people who are active in fewer but longer bouts (lower graph). It's clear that these are two extreme ends of a continuous scale of activity patterns with anything in between and combinations of the two patterns are possible.

Activity

Question: How could the "clumpiness" of the activity patterns be quantified?

I thought of some form of entropy but I'm not sure if that would capture these patterns accurately.

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    $\begingroup$ My first impulse would be to integrate the absolute value of second differences, possibly after smoothing. $\endgroup$ Commented Mar 22 at 9:07
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    $\begingroup$ A simple solution: Set a threshold of activity and define a 'bout' as contiguous time spent over threshold. Then you can quantify 'number of bouts per day' and 'average duration of bout' (maybe also variance in duration could be interesting). $\endgroup$
    – MKR
    Commented Mar 22 at 10:05

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