code: def test_nan():
      """
      This is a very slow test to check that the distribution of simulated states
      (from the posterior) is correct in the presense of NaN values. Here, it
      checks the marginal distribution of the drawn states against the values
      computed from the smoother and prints the result.
  
      With the fixed simulation smoother, it prints:
  
      True values:
      [1.         0.66666667 0.66666667 1.        ]
      [0.         0.95238095 0.95238095 0.        ]
  
      Simulated values:
      [1.         0.66699187 0.66456719 1.        ]
      [0.       0.953608 0.953198 0.      ]
  
      Previously, it would have printed:
  
      True values:
      [1.         0.66666667 0.66666667 1.        ]
      [0.         0.95238095 0.95238095 0.        ]
  
      Simulated values:
      [1.         0.66666667 0.66666667 1.        ]
      [0. 0. 0. 0.]
      """
      return
      mod = sarimax.SARIMAX(
          [1, np.nan, np.nan, 1], order=(1, 0, 0), trend="c"
      )
      res = mod.smooth([0, 0.5, 1.0])
  
      rs = np.random.RandomState(1234)
      sim = mod.simulation_smoother(random_state=rs)
  
      n = 1000000
      out = np.zeros((n, mod.nobs))
      for i in range(n):
          sim.simulate()
          out[i] = sim.simulated_state
  
      print("True values:")
      print(res.smoothed_state[0])
      print(res.smoothed_state_cov[0, 0])
      print()
      print("Simulated values:")
      print(np.mean(out, axis=0))
      print(np.var(out, axis=0).round(6))
  
imports: import os
  import numpy
  import pandas
  from numpy.testing import assert_allclose, assert_equal
  import pytest
  from statsmodels import datasets
  from statsmodels.tsa.statespace import mlemodel, sarimax, structural, varmax
  from statsmodels.tsa.statespace.simulation_smoother import SIMULATION_STATE, SIMULATION_DISTURBANCE, SIMULATION_ALL
label_desc: Use image node_id 7 for calling a global function with example usage: test_nan() without return types