code: def test_get_distribution():
      np.random.seed(234)
  
      n = 100
      n_groups = 10
      fe_params = np.r_[1, -2]
      cov_re = np.asarray([[1, 0.5], [0.5, 2]])
      vcomp = np.r_[0.5**2, 1.5**2]
      scale = 1.5
  
      exog_fe = np.random.normal(size=(n, 2))
      exog_re = np.random.normal(size=(n, 2))
      exog_vca = np.random.normal(size=(n, 2))
      exog_vcb = np.random.normal(size=(n, 2))
  
      groups = np.repeat(np.arange(n_groups, dtype=int), n / n_groups)
  
      ey = np.dot(exog_fe, fe_params)
  
      u = np.random.normal(size=(n_groups, 2))
      u = np.dot(u, np.linalg.cholesky(cov_re).T)
  
      u1 = np.sqrt(vcomp[0]) * np.random.normal(size=(n_groups, 2))
      u2 = np.sqrt(vcomp[1]) * np.random.normal(size=(n_groups, 2))
  
      y = ey + (u[groups, :] * exog_re).sum(1)
      y += (u1[groups, :] * exog_vca).sum(1)
      y += (u2[groups, :] * exog_vcb).sum(1)
      y += np.sqrt(scale) * np.random.normal(size=n)
  
      df = pd.DataFrame(
          {
              "y": y,
              "x1": exog_fe[:, 0],
              "x2": exog_fe[:, 1],
              "z0": exog_re[:, 0],
              "z1": exog_re[:, 1],
              "grp": groups,
          }
      )
      df["z2"] = exog_vca[:, 0]
      df["z3"] = exog_vca[:, 1]
      df["z4"] = exog_vcb[:, 0]
      df["z5"] = exog_vcb[:, 1]
  
      vcf = {"a": "0 + z2 + z3", "b": "0 + z4 + z5"}
      m = MixedLM.from_formula(
          "y ~ 0 + x1 + x2",
          groups="grp",
          re_formula="0 + z0 + z1",
          vc_formula=vcf,
          data=df,
      )
  
      # Build a params vector that is comparable to
      # MixedLMResults.params
      import statsmodels
  
      mp = statsmodels.regression.mixed_linear_model.MixedLMParams
      po = mp.from_components(
          fe_params=fe_params, cov_re=cov_re, vcomp=vcomp
      )
      pa = po.get_packed(has_fe=True, use_sqrt=False)
      pa[len(fe_params) :] /= scale
  
      # Get a realization
      dist = m.get_distribution(pa, scale, None)
      yr = dist.rvs(0)
  
      # Check the overall variance
      v = (np.dot(exog_re, cov_re) * exog_re).sum(1).mean()
      v += vcomp[0] * (exog_vca**2).sum(1).mean()
      v += vcomp[1] * (exog_vcb**2).sum(1).mean()
      v += scale
      assert_allclose(np.var(yr - ey), v, rtol=1e-2, atol=1e-4)
  
imports: from statsmodels.compat.platform import PLATFORM_OSX
  import os
  import csv
  import warnings
  import numpy
  import pandas
  from scipy import sparse
  import pytest
  from statsmodels.regression.mixed_linear_model import MixedLM, MixedLMParams, _smw_solver, _smw_logdet
  from numpy.testing import assert_almost_equal, assert_equal, assert_allclose, assert_
  from statsmodels.base import _penalties
  import statsmodels.tools.numdiff
  from .results import lme_r_results
label_desc: Use image node_id 12 for calling a global function with example usage: test_get_distribution() without return types