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I have data for several individuals that takes the following form over time. Many individuals are flat over the course of a year, meaning their measurements stay roughly the same. Others have a peak or two and are then flat. And others have many peaks. For each individual I must find an average (representative) value that is not influenced by the peaks. For example, the overall average will not be a good measure because if an individual has several peaks, this will increase the average. Overall, I need an estimate of the baseline for each individual that is not influenced by the number of peaks an individual has.

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    $\begingroup$ Hi Julieth, I want to know how does you solved this. I have the same issue as posted on datascience.stackexchange.com/q/11973/13291 $\endgroup$ – Haroon Rashid May 28 '16 at 9:43
  • $\begingroup$ "For example, the overall average will not be a good measure because if an individual has several peaks, this will increase the average." This is precisely why I think the average is a good summary measure. If it's blood pressure, those "peaks" let doctors know you have hypertension. $\endgroup$ – AdamO Jan 9 '20 at 14:43
  • $\begingroup$ If you provide a couple of plots of the time series and the values that you want to get out, it is easier for people to give you good answers. $\endgroup$ – Jon Nordby Sep 10 '20 at 20:35
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Probably the first step would be thinking about how to define what one of your peaks is mathematically. E.g., maybe a peak in your case contains values greater than X% of the other values for each individual. At that point it would be easy to calculate the Xth percentile for the value for each individual using any statistical software.

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If you are looking for a "representative" outcome that is robust to occasional large deviations, an obvious candidate would be the mode of the distribution. If your time-series data takes on discrete values and there is substantial repitition then it would be possible to estimate these values empirically; if the time-series data is continuous then you could form an appropriate kernel density estimator and estimate the mode as the value that maximises the estimated density.

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