code: def examples_normexpand():
      skewnorm = SkewNorm_gen()
      rvs = skewnorm.rvs(5, size=100)
      normexpan = NormExpan_gen(rvs, mode="sample")
  
      smvsk = stats.describe(rvs)[2:]
      print("sample: mu,sig,sk,kur")
      print(smvsk)
  
      dmvsk = normexpan.stats(moments="mvsk")
      print("normexpan: mu,sig,sk,kur")
      print(dmvsk)
      print("mvsk diff distribution - sample")
      print(np.array(dmvsk) - np.array(smvsk))
      print("normexpan attributes mvsk")
      print(mc2mvsk(normexpan.cnt))
      print(normexpan.mvsk)
  
      mnc = mvsk2mnc(dmvsk)
      mc = mnc2mc(mnc)
      print("central moments")
      print(mc)
      print("non-central moments")
      print(mnc)
  
      pdffn = pdf_moments(mc)
      print("\npdf approximation from moments")
      print("pdf at", mc[0] - 1, mc[0] + 1)
      print(pdffn([mc[0] - 1, mc[0] + 1]))
      print(normexpan.pdf([mc[0] - 1, mc[0] + 1]))
  
file_path: statsmodels/statsmodels/sandbox/distributions/examples/ex_extras.py
imports: import numpy
  from scipy import stats
  from statsmodels.sandbox.distributions.extras import SkewNorm_gen, skewnorm, ACSkewT_gen, NormExpan_gen, pdf_moments, ExpTransf_gen, LogTransf_gen
  from statsmodels.stats.moment_helpers import mc2mvsk, mnc2mc, mvsk2mnc
label_desc: Use image node_id 3 for calling a global function with example usage: examples_normexpand() without return types