Error in scipy.stats.mannwhitneyu documentation

Below is the docstring of the scipy.stats.mannwhitneyu function (scipy==1.8.0) If F(u) and G(u) are the cumulative distribution functions of the distributions underlying x and y, respectively then the hypothesis for ‘greater’ would be F(u) > G(u) for all u, right?. However, in the documentation, the inequality is written in the other direction. And the same for the ‘less’ hypothesis.

Parameters
----------
x, y : array-like
    N-d arrays of samples. The arrays must be broadcastable except along
    the dimension given by `axis`.
use_continuity : bool, optional
    Whether a continuity correction (1/2) should be applied.
    Default is True when `method` is ``'asymptotic'``; has no effect
    otherwise.
alternative : {'two-sided', 'less', 'greater'}, optional
    Defines the alternative hypothesis. Default is 'two-sided'.
    Let *F(u)* and *G(u)* be the cumulative distribution functions of the
    distributions underlying `x` and `y`, respectively. Then the following
    alternative hypotheses are available:
    
    * 'two-sided': the distributions are not equal, i.e. *F(u) ≠ G(u)* for
      at least one *u*.
    * 'less': the distribution underlying `x` is stochastically less
      than the distribution underlying `y`, i.e. *F(u) > G(u)* for all *u*.
    * 'greater': the distribution underlying `x` is stochastically greater
      than the distribution underlying `y`, i.e. *F(u) < G(u)* for all *u*.

[tupui]

Documentation improvement are always welcomed.

[mdhaber]

For reference, SciPy’s description of the alternatives is directly from the original paper: