`scipy.stats._stats_py:_cdf_distance`

source: /scipy/stats/_stats_py.py :9774

Signature

   def     _cdf_distance (    p    ,    u_values    ,    v_values    ,    u_weights    =  None   ,    v_weights    =  None     )

Summary

Compute, between two one-dimensional distributions $u$ and $v$ , whose respective CDFs are $U$ and $V$ , the statistical distance that is defined as:

Extended Summary

l_{p} (u, v) = (\int_{- \infty}^{+ \infty} ∣ U - V ∣^{p})^{1/ p}

p is a positive parameter; p = 1 gives the Wasserstein distance, p = 2 gives the energy distance.

Parameters

u_values, v_values : array_like: Values observed in the (empirical) distribution.
u_weights, v_weights : array_like, optional: Weight for each value. If unspecified, each value is assigned the same weight. u_weights (resp. v_weights) must have the same length as u_values (resp. v_values). If the weight sum differs from 1, it must still be positive and finite so that the weights can be normalized to sum to 1.

Returns

distance : float: The computed distance between the distributions.

Notes

The input distributions can be empirical, therefore coming from samples whose values are effectively inputs of the function, or they can be seen as generalized functions, in which case they are weighted sums of Dirac delta functions located at the specified values.

Aliases

scipy.stats._stats_py._cdf_distance