code: def _fitstart_poisson(self, x, fixed=None):
      """maximum likelihood estimator as starting values for Poisson distribution
  
      Parameters
      ----------
      x : ndarray
          data for which the parameters are estimated
      fixed : None or array_like
          sequence of numbers and np.nan to indicate fixed parameters and parameters
          to estimate
  
      Returns
      -------
      est : tuple
          preliminary estimates used as starting value for fitting, not
          necessarily a consistent estimator
  
      Notes
      -----
      This needs to be written and attached to each individual distribution
  
      References
      ----------
      MLE :
      https://en.wikipedia.org/wiki/Poisson_distribution#Maximum_likelihood
  
      """
      # todo: separate out this part to be used for other compact support distributions
      #      e.g. rdist, vonmises, and truncnorm
      #      but this might not work because it might still be distribution specific
      a = x.min()
      eps = 0  # is this robust ?
      if fixed is None:
          # this part not checked with books
          loc = a - eps
      else:
          if np.isnan(fixed[-1]):
              # estimate loc
              loc = a - eps
          else:
              loc = fixed[-1]
  
      # MLE for standard (unshifted, if loc=0) Poisson distribution
  
      xtrans = x - loc
      lambd = xtrans.mean()
      # second derivative d loglike/ dlambd Not used
      # dlldlambd = 1/lambd # check
  
      return (lambd, loc)
  
file_path: statsmodels/statsmodels/sandbox/distributions/sppatch.py
imports: from statsmodels.compat.python import lmap
  import numpy
  from scipy import stats, optimize, integrate
label_desc: Use image node_id 3 for calling a global function with example usage: _fitstart_poisson(x, fixed) and returns: lambd,  loc