Given the data as follows,

Oridata = {5,19,24,22,23,20,14,11,13,15,11,8,7,5,5,4,4,3,2,2,1,1,0,0,0,0,0}

CumData = {5, 24, 48, 70, 93, 113, 127, 138, 151, 166, 177, 185, 192, 197, 202,
206, 210, 213, 215, 217, 218, 219, 219, 219, 219, 219, 219}  
(*cumulative data for process fitting*)

I am receiving the follwing error when i am considering CumData for CompoundPoissonProcess[$\lambda$, LogSeriesDistribution[$\theta$]]]

EstimatedProcess::ntsprt: One or more data points are not in the support of the process CompoundPoissonProcess[$\lambda$,LogSeriesDistribution[$\theta$]]

But with the same CumData if applied as

EstimatedProcess[CumData,CompoundPoissonProcess[$\lambda$,PoissonDistribution[ $\phi$]]]. It estimated as


If further check with a different model,

EstimatedProcess[CumData,CompoundPoissonProcess[$\lambda$,NegativeBinomialDistribution[ $n,p$]]].

It estimated as


I'm wondering why in later cases there are no errors.

Kindly assist, what causes an such error and how to use CumData for parameter estimation for CompoundPoissonProcess[$\lambda$,LogSeriesDistribution[$\theta$]].

  • 2
    $\begingroup$ It seems to happen because of the duplicate 219 elements in your cumulative data. Zero isn't in the support of LogSeriesDistribution. You cannot fit a CompoundPoissonProcess with a non-zero jump size distribution because the last six elements of your data have no jumps. $\endgroup$ – flinty Jun 9 '20 at 8:34
  • $\begingroup$ @flinty thanks. This is valuable information for me. Now i tried, with CumData[[1 ;; -5]], it estimated as CompoundPoissonProcess[1., LogSeriesDistribution[0.973749]]. Would it be the right approach to reduce data points? If no, then any other alternative will be appreciated. $\endgroup$ – step-by-step Jun 9 '20 at 9:06
  • $\begingroup$ If you generate some paths from the process e.g with RandomFunction[ CompoundPoissonProcess[1., LogSeriesDistribution[0.973749]], {50}]["Values"] do they look reasonable to you? I don't know what physical thing your data represents so I couldn't comment on whether its right to exclude those points - but if you expect zero jumps in your data you may want a more appropriate distribution that allows it. $\endgroup$ – flinty Jun 9 '20 at 9:12
  • $\begingroup$ Indeed, I didnt get effective mean near to 219 if Mean@(RandomFunction[ CompoundPoissonProcess[1., LogSeriesDistribution[0.973749]], {50},1000]["LastValues"]). Possibly the estimation way might not appropirate. But I required this model only for some reason. $\endgroup$ – step-by-step Jun 9 '20 at 10:51

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