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I have done some statistical distributions on real-world data. The distribution fitting gives me the below results (lognormal fits the best on data based on chi-squared test):

Best Distribution fits with parameters:
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Distribution: lognorm
Parameters: (0.5921510072108613, -0.006454418407435666, 0.021090953536473916)

Distribution: expon
Parameters: (2e-06, 0.018877666177431276)

Distribution: pareto
Parameters: (11.057961210885452, -0.20440106940633995, 0.20436985884797232)

Here, i want to achieve two things:

  • Using the best parameters,how to generate the new synthetic data that represent our original data?. Does the rvs method in python is useful?

  • Compare the actual and generated data distribution fitting as shown in below figure.

enter image description here

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  • $\begingroup$ Yes. The rvs method will be useful. If you have decided to use lognormal distribution, you can check docs.scipy.org/doc/scipy/reference/generated/… for specific examples of generating random numbers. $\endgroup$
    – hssay
    Commented Dec 5, 2019 at 6:40
  • $\begingroup$ You can use Kullback-Leibler metric to compare distributions. $\endgroup$
    – Piotr Rarus
    Commented Dec 5, 2019 at 8:49

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Good question. Lots of options.

Most would recommend you use CDFs instead of histograms. So convert your observed distribution to empirical CDF (in R it’s ecdf() - I dint know python). Then, plot another line that is the theoretical CDF using your best-fit parameters over the span of a to b, where a to b gives you at least the same coverage as your original data set limits.

Alternatively you could go for a chi-square option that’ll give you observed vs predicted and can be plotted as histogram but I don’t find that better in most cases, though it might make quantitative comparison more accessible

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  • $\begingroup$ Just to add a bit on @HEITS: To plot CDF for Python, you can go through this link. $\endgroup$
    – Toros91
    Commented Dec 5, 2019 at 7:59

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