Thank you very much for your kind suggestion above. However, after I did as per your suggestion, I found out many issues as following: First of all, please let me clarify you that the data range of this fitted Pareto distribution is 300,000-800,000 (with theta =300,000). And then I simulated Pareto distribution without identifying theta. After I used the coding to add theta as per your suggestion, I think that the output statistic seems worse. Kindly find the compared statistic as below details: Fitting Pareto distribution -> output1 Simulation without theta -> output2 (after cut off data, so the data range of is 300,000-800,000) Simulation with theta -> output3 (after cut off data, so the data range of is 300,000-800,000) As you can see that, the statistic of simulation with theta are different from the fitted Pareto quite much. I am not sure if these output are acceptable or not? If not, please let have your further suggestion.
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