class_docstr: Simulate exchangeable Poisson data.
  
  The data within a cluster are simulated as y_i = z_c + z_i.  The
  z_c, and {z_i} are independent Poisson random variables with
  expected values e_c and {e_i}, respectively.  In order for the
  pairwise correlation to be equal to `f` for all pairs, we need
  
       e_c / sqrt((e_c + e_i) * (e_c + e_j)) = f for all i, j.
  
  By setting all e_i = e within a cluster, these equations can be
  satisfied.  We thus need
  
       e_c * (1 - f) = f * e,
  
  which can be solved (non-uniquely) for e and e_c.
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code: def print_dparams(self, dparams_est):
      OUT.write(
          "Estimated common pairwise correlation:   %8.4f\n"
          % dparams_est[0]
      )
      OUT.write(
          "True common pairwise correlation:        %8.4f\n"
          % self.dparams[0]
      )
      OUT.write(
          "Estimated inverse scale parameter:       %8.4f\n"
          % dparams_est[1]
      )
      OUT.write(
          "True inverse scale parameter:            %8.4f\n"
          % self.scale_inv
      )
      OUT.write("\n")
  
file_path: statsmodels/statsmodels/genmod/tests/gee_poisson_simulation_check.py
imports: import numpy
  from statsmodels.genmod.families import Poisson
  from .gee_gaussian_simulation_check import GEE_simulator
  from statsmodels.genmod.generalized_estimating_equations import GEE
  from statsmodels.genmod.cov_struct import Exchangeable, Independence
label_desc: Use image node_id 1 for calling the Exchangeable_simulator obj's underlying member method code with example usage: obj.print_dparams(dparams_est) without return types