class_docstr: Class for the manifold of Poisson distributions.
  
  This is the parameter space of Poisson distributions
  i.e. [the half-line of positive reals].
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docstr: Evaluate if a point belongs to the manifold of Poisson distributions.
  
  Parameters
  ----------
  point : array-like, shape=[..., 1]
      Point to be checked.
  atol : float
      Tolerance to evaluate positivity.
      Optional, default: gs.atol
  
  Returns
  -------
  belongs : array-like, shape=[...,]
      Boolean indicating whether point represents an Poisson
      distribution.
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code: def belongs(self, point, atol=gs.atol):
      """Evaluate if a point belongs to the manifold of Poisson distributions.
  
      Parameters
      ----------
      point : array-like, shape=[..., 1]
          Point to be checked.
      atol : float
          Tolerance to evaluate positivity.
          Optional, default: gs.atol
  
      Returns
      -------
      belongs : array-like, shape=[...,]
          Boolean indicating whether point represents an Poisson
          distribution.
      """
      belongs_shape = self.shape == point.shape[-self.point_ndim :]
      if not belongs_shape:
          shape = point.shape[: -self.point_ndim]
          return gs.zeros(shape, dtype=bool)
      return gs.squeeze(point >= -atol)
  
imports: from scipy.special import factorial
  from scipy.stats import poisson
  import geomstats.backend
  from geomstats.geometry.base import VectorSpaceOpenSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.information_geometry.base import InformationManifoldMixin, ScipyUnivariateRandomVariable
label_desc: Use image node_id 3 for calling the PoissonDistributions obj's underlying member method code with example usage: obj.belongs(point, atol) and returns: gs, gs