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: Project a point in ambient space to the open set.
  
  Return a point belonging to the half-line of positive reals
  within the given tolerance.
  
  Parameters
  ----------
  point : array-like, shape=[..., 1]
      Point in ambient space.
  atol : float
      Tolerance to evaluate positivity.
  
  Returns
  -------
  projected : array-like, shape=[..., 1]
      Projected point.
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code: def projection(self, point, atol=gs.atol):
      """Project a point in ambient space to the open set.
  
      Return a point belonging to the half-line of positive reals
      within the given tolerance.
  
      Parameters
      ----------
      point : array-like, shape=[..., 1]
          Point in ambient space.
      atol : float
          Tolerance to evaluate positivity.
  
      Returns
      -------
      projected : array-like, shape=[..., 1]
          Projected point.
      """
      return gs.where(point < atol, atol, point)
  
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 5 for calling the PoissonDistributions obj's underlying member method code with example usage: obj.projection(point, atol) and returns: gs