From 847010aeecbbf9e513530a1d772a13ee0ee3e15c Mon Sep 17 00:00:00 2001
From: chrisb83 <christoph.baumgarten@gmail.com>
Date: Sun, 18 Aug 2019 19:27:39 +0200
Subject: [PATCH] MAINT: link rdist and semicircular in scipy.stats

stats.semicircular is a special case of rdist with c=3
---
 scipy/stats/_continuous_distns.py       | 19 ++++++++++++++++---
 scipy/stats/_distr_params.py            |  2 +-
 scipy/stats/tests/test_distributions.py |  2 +-
 3 files changed, 18 insertions(+), 5 deletions(-)

diff --git a/scipy/stats/_continuous_distns.py b/scipy/stats/_continuous_distns.py
index 7002c62bc79e..96a58ff2fae2 100644
--- a/scipy/stats/_continuous_distns.py
+++ b/scipy/stats/_continuous_distns.py
@@ -5950,6 +5950,7 @@ class rdist_gen(rv_continuous):
     special cases::
 
         c = 2:  uniform
+        c = 3:  `semicircular`
         c = 4:  Epanechnikov (parabolic)
         c = 6:  quartic (biweight)
         c = 8:  triweight
@@ -5961,13 +5962,13 @@ class rdist_gen(rv_continuous):
     """
     # use relation to the beta distribution for pdf, cdf, etc
     def _pdf(self, x, c):
-        return 0.5*beta._pdf((x+1)/2, c/2, c/2)
+        return 0.5*beta._pdf((x + 1)/2, c/2, c/2)
 
     def _logpdf(self, x, c):
-        return -np.log(2) + beta._logpdf((x+1)/2, c/2, c/2)
+        return -np.log(2) + beta._logpdf((x + 1)/2, c/2, c/2)
 
     def _cdf(self, x, c):
-        return beta._cdf((x+1)/2, c/2, c/2)
+        return beta._cdf((x + 1)/2, c/2, c/2)
 
     def _ppf(self, q, c):
         return 2*beta._ppf(q, c/2, c/2) - 1
@@ -6222,8 +6223,14 @@ class semicircular_gen(rv_continuous):
 
     for :math:`-1 \le x \le 1`.
 
+    The distribution is a special case of `rdist` with `c = 3`.
+
     %(after_notes)s
 
+    See Also
+    --------
+    rdist
+
     References
     ----------
     .. [1] "Wigner semicircle distribution",
@@ -6235,9 +6242,15 @@ class semicircular_gen(rv_continuous):
     def _pdf(self, x):
         return 2.0/np.pi*np.sqrt(1-x*x)
 
+    def _logpdf(self, x):
+        return np.log(2/np.pi) + 0.5*np.log1p(-x*x)
+
     def _cdf(self, x):
         return 0.5+1.0/np.pi*(x*np.sqrt(1-x*x) + np.arcsin(x))
 
+    def _ppf(self, q):
+        return rdist._ppf(q, 3)
+
     def _rvs(self):
         # generate values uniformly distributed on the area under the pdf
         # (semi-circle) by randomly generating the radius and angle
diff --git a/scipy/stats/_distr_params.py b/scipy/stats/_distr_params.py
index 52976ecdc776..37e696fd65fe 100644
--- a/scipy/stats/_distr_params.py
+++ b/scipy/stats/_distr_params.py
@@ -87,7 +87,7 @@
     ['powerlognorm', (2.1413923530064087, 0.44639540782048337)],
     ['powernorm', (4.4453652254590779,)],
     ['rayleigh', ()],
-    ['rdist', (0.9,)],   # feels also slow
+    ['rdist', (1.6,)],
     ['recipinvgauss', (0.63004267809369119,)],
     ['reciprocal', (0.0062309367010521255, 1.0062309367010522)],
     ['rice', (0.7749725210111873,)],
diff --git a/scipy/stats/tests/test_distributions.py b/scipy/stats/tests/test_distributions.py
index d49317ef6708..bc376e3b8713 100644
--- a/scipy/stats/tests/test_distributions.py
+++ b/scipy/stats/tests/test_distributions.py
@@ -2754,7 +2754,7 @@ def test_rdist_beta(self):
         # rdist is a special case of stats.beta
         x = np.linspace(-0.99, 0.99, 10)
         c = 2.7
-        assert_almost_equal(0.5*stats.beta(c/2, c/2).pdf((x+1)/2),
+        assert_almost_equal(0.5*stats.beta(c/2, c/2).pdf((x + 1)/2),
                             stats.rdist(c).pdf(x))