Use Databin to Store Time Series

The arrival times in a PoissonProcess are independent and follow an ExponentialDistribution. You can simulate a path of a PoissonProcess by sending signals to a Databin in time intervals specified by a simulation of an exponential distribution.

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SeedRandom["11"]; \[Lambda] = 0.5; times = RandomVariate[ExponentialDistribution[\[Lambda]], 30];

Create a Databin.

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bin = CreateDatabin[]

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Use the simulated times to send 1 to the databin in time intervals.

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Table[DatabinAdd[bin, <|"arrivals" -> 1|>]; Pause[t], {t, times}];

The recorded signal with the time stamps.

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TimeSeries[bin]

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Extract the TimeSeries object.

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ts1 = TimeSeries[bin]["arrivals"]

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This time series is irregularly sampled.

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RegularlySampledQ[ts1]

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Assume TemporalRegularity so that Accumulate does not use interpolation to resample the time series with respect to the minimum time increment.

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ts2 = Accumulate[TimeSeries[ts1, TemporalRegularity -> True]]

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DateListStepPlot[ts2, Joined -> False, PlotTheme -> "Detailed"]

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Estimate the PoissonProcess parameter from the signal and compare to the parameter of the ExponentialDistribution used to simulate time stamps.

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{FindProcessParameters[ts2, PoissonProcess[\[Mu]]], \[Lambda]}

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