class_docstr: Class for the manifold of multinomial distributions.
  
  This is the set of `n+1`-tuples of positive reals that sum up to one,
  i.e. the `n`-simplex. Each point is the parameter of a multinomial
  distribution, i.e. gives the probabilities of $n$ different outcomes
  in a single experiment.
  
  Attributes
  ----------
  dim : int
      Dimension of the parameter manifold of multinomial distributions.
      The number of outcomes is dim + 1.
  embedding_manifold : Manifold
      Embedding manifold.
docstr: Metric to equip the space with if equip is True.
docstr_tok: ["Metric","to","equip","the","space","with","if","equip","is","True","."]
code: def default_metric():
      """Metric to equip the space with if equip is True."""
      return MultinomialMetric
  
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 2 for calling the MultinomialDistributions obj's underlying member method code with example usage: obj.default_metric() and returns: MultinomialMetric