DOC: fix name of shape parameter kappa of von Mises distribution (numpy#27721)

* Fix name of shape parameter kappa of von Mises distribution

The parameter kappa in the equation of the von Mises distribution is not the dispersion but its reciprocal. This is typically referred to as the concentration (see for example https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.vonmises.html). Change the docstring of the `vonmises` method in `_generator.pyx` and `mtrand.pyx` accordingly.

Author: simonaltrogge

numpy/random/_generator.pyx

@@ -1977,7 +1977,7 @@ cdef class Generator:
         Draw samples from a von Mises distribution.
 
         Samples are drawn from a von Mises distribution with specified mode
-        (mu) and dispersion (kappa), on the interval [-pi, pi].
+        (mu) and concentration (kappa), on the interval [-pi, pi].
 
         The von Mises distribution (also known as the circular normal
         distribution) is a continuous probability distribution on the unit
@@ -1989,7 +1989,7 @@ cdef class Generator:
         mu : float or array_like of floats
             Mode ("center") of the distribution.
         kappa : float or array_like of floats
-            Dispersion of the distribution, has to be >=0.
+            Concentration of the distribution, has to be >=0.
         size : int or tuple of ints, optional
             Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
             ``m * n * k`` samples are drawn.  If size is ``None`` (default),
@@ -2012,7 +2012,7 @@ cdef class Generator:
 
         .. math:: p(x) = \\frac{e^{\\kappa cos(x-\\mu)}}{2\\pi I_0(\\kappa)},
 
-        where :math:`\\mu` is the mode and :math:`\\kappa` the dispersion,
+        where :math:`\\mu` is the mode and :math:`\\kappa` the concentration,
         and :math:`I_0(\\kappa)` is the modified Bessel function of order 0.
 
         The von Mises is named for Richard Edler von Mises, who was born in
@@ -2033,7 +2033,7 @@ cdef class Generator:
         --------
         Draw samples from the distribution:
 
-        >>> mu, kappa = 0.0, 4.0 # mean and dispersion
+        >>> mu, kappa = 0.0, 4.0 # mean and concentration
         >>> rng = np.random.default_rng()
         >>> s = rng.vonmises(mu, kappa, 1000)
 

numpy/random/mtrand.pyx

@@ -2282,7 +2282,7 @@ cdef class RandomState:
         Draw samples from a von Mises distribution.
 
         Samples are drawn from a von Mises distribution with specified mode
-        (mu) and dispersion (kappa), on the interval [-pi, pi].
+        (mu) and concentration (kappa), on the interval [-pi, pi].
 
         The von Mises distribution (also known as the circular normal
         distribution) is a continuous probability distribution on the unit
@@ -2299,7 +2299,7 @@ cdef class RandomState:
         mu : float or array_like of floats
             Mode ("center") of the distribution.
         kappa : float or array_like of floats
-            Dispersion of the distribution, has to be >=0.
+            Concentration of the distribution, has to be >=0.
         size : int or tuple of ints, optional
             Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
             ``m * n * k`` samples are drawn.  If size is ``None`` (default),
@@ -2323,7 +2323,7 @@ cdef class RandomState:
 
         .. math:: p(x) = \\frac{e^{\\kappa cos(x-\\mu)}}{2\\pi I_0(\\kappa)},
 
-        where :math:`\\mu` is the mode and :math:`\\kappa` the dispersion,
+        where :math:`\\mu` is the mode and :math:`\\kappa` the concentration,
         and :math:`I_0(\\kappa)` is the modified Bessel function of order 0.
 
         The von Mises is named for Richard Edler von Mises, who was born in
@@ -2344,7 +2344,7 @@ cdef class RandomState:
         --------
         Draw samples from the distribution:
 
-        >>> mu, kappa = 0.0, 4.0 # mean and dispersion
+        >>> mu, kappa = 0.0, 4.0 # mean and concentration
         >>> s = np.random.vonmises(mu, kappa, 1000)
 
         Display the histogram of the samples, along with