diff --git a/pymc/distributions/continuous.py b/pymc/distributions/continuous.py
index d597299997..e5efeb775a 100644
--- a/pymc/distributions/continuous.py
+++ b/pymc/distributions/continuous.py
@@ -1714,7 +1714,6 @@ def logcdf(value, mu, sigma):
             -np.inf,
             normal_lcdf(mu, sigma, pt.log(value)),
         )
-
         return check_parameters(
             res,
             sigma > 0,
@@ -2039,6 +2038,15 @@ def logcdf(value, alpha, beta):
             msg="beta > 0",
         )
 
+    def icdf(value, alpha, beta):
+        res = alpha + beta * pt.tan(np.pi * (value - 0.5))
+        res = check_icdf_value(res, value)
+        return check_parameters(
+            res,
+            beta > 0,
+            msg="beta > 0",
+        )
+
 
 class HalfCauchy(PositiveContinuous):
     r"""
@@ -3357,6 +3365,15 @@ def logcdf(value, mu, s):
             msg="s > 0",
         )
 
+    def icdf(value, mu, s):
+        res = mu + s * pt.log(value / (1 - value))
+        res = check_icdf_value(res, value)
+        return check_parameters(
+            res,
+            s > 0,
+            msg="s > 0",
+        )
+
 
 class LogitNormalRV(RandomVariable):
     name = "logit_normal"
diff --git a/tests/distributions/test_continuous.py b/tests/distributions/test_continuous.py
index b84a77e049..a4512b8a61 100644
--- a/tests/distributions/test_continuous.py
+++ b/tests/distributions/test_continuous.py
@@ -548,6 +548,11 @@ def test_cauchy(self):
             {"alpha": R, "beta": Rplusbig},
             lambda value, alpha, beta: st.cauchy.logcdf(value, alpha, beta),
         )
+        check_icdf(
+            pm.Cauchy,
+            {"alpha": R, "beta": Rplusbig},
+            lambda q, alpha, beta: st.cauchy.ppf(q, alpha, beta),
+        )
 
     def test_half_cauchy(self):
         check_logp(
@@ -768,6 +773,12 @@ def test_logistic(self):
             lambda value, mu, s: st.logistic.logcdf(value, mu, s),
             decimal=select_by_precision(float64=6, float32=1),
         )
+        check_icdf(
+            pm.Logistic,
+            {"mu": R, "s": Rplus},
+            lambda q, mu, s: st.logistic.ppf(q, mu, s),
+            decimal=select_by_precision(float64=6, float32=1),
+        )
 
     def test_logitnormal(self):
         check_logp(