class_docstr: Class for the Fisher information metric on multinomial distributions.
  
  The Fisher information metric on the $n$-simplex of multinomial
  distributions parameters can be obtained as the pullback metric of the
  $n$-sphere using the componentwise square root.
  
  References
  ----------
  .. [K2003] R. E. Kass. The Geometry of Asymptotic Inference. Statistical
      Science, 4(3): 188 - 234, 1989.
code: def __init__(self, space):
      super().__init__(space)
      self._sphere = Hypersphere(dim=space.dim)
  
imports: from scipy.stats import dirichlet, multinomial
  import geomstats.backend
  from geomstats.algebra_utils import from_vector_to_diagonal_matrix
  from geomstats.geometry.base import LevelSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.hypersphere import Hypersphere
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.information_geometry.base import InformationManifoldMixin, ScipyMultivariateRandomVariable
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 1 to create a new MultinomialMetric object from inherited base classes: RiemannianMetric with example: obj = MultinomialMetric(space)