class_docstr: Class for the Fisher information metric on Poisson distributions.
  
  References
  ----------
  .. [AM1981] Atkinson, C., & Mitchell, A. F. (1981). Rao's distance measure.
      Sankhyā: The Indian Journal of Statistics, Series A, 345-365.
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docstr: Generate parameterized function for geodesic curve.
  
  Parameters
  ----------
  t : array-like, shape=[n_times,]
      Times at which to compute points of the geodesics.
  
  Returns
  -------
  geodesic : array-like, shape=[..., n_times, 1]
      Values of the geodesic at times t.
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code: def _geodesic_path(t, constant_a, constant_b):
      """Generate parameterized function for geodesic curve.
  
      Parameters
      ----------
      t : array-like, shape=[n_times,]
          Times at which to compute points of the geodesics.
  
      Returns
      -------
      geodesic : array-like, shape=[..., n_times, 1]
          Values of the geodesic at times t.
      """
      return gs.expand_dims((constant_a * t + constant_b) ** 2, axis=-1)
  
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 PoissonMetric obj's underlying member method code with example usage: obj._geodesic_path(t, constant_a, constant_b) and returns: gs