Implement log CDF for Cauchy distribution

Author: domenzain

pymc3/distributions/continuous.py

@@ -870,6 +870,9 @@ def logp(self, value):
                      - tt.log1p(((value - alpha) / beta)**2),
                      beta > 0)
 
+    def logcdf (self, value):
+          return tt.log(0.5 + tt.arctan ((value - self.alpha) / self.beta) / np.pi)
+
 
 class HalfCauchy(PositiveContinuous):
     R"""

pymc3/tests/test_distributions.py

@@ -471,6 +471,8 @@ def test_t(self):
     def test_cauchy(self):
         self.pymc3_matches_scipy(Cauchy, R, {'alpha': R, 'beta': Rplusbig},
                                  lambda value, alpha, beta: sp.cauchy.logpdf(value, alpha, beta))
+        self.check_logcdf(Cauchy, R, {'alpha': R, 'beta': Rplusbig},
+                          lambda value, alpha, beta: sp.cauchy.logcdf(value, alpha, beta))
 
     def test_half_cauchy(self):
         self.pymc3_matches_scipy(HalfCauchy, Rplus, {'beta': Rplusbig},