diff --git a/pymc3/distributions/continuous.py b/pymc3/distributions/continuous.py
index 88cff6779f..c60898ab16 100644
--- a/pymc3/distributions/continuous.py
+++ b/pymc3/distributions/continuous.py
@@ -1669,14 +1669,14 @@ class AsymmetricLaplace(Continuous):
     The pdf of this distribution is
 
     .. math::
-        {f(x|\\b,\kappa) =
-            \left({\frac{\\b}{\kappa + 1/\kappa}}\right)\,e^{-(x)\\b\,s\kappa ^{s}}}
+        {f(x|\\b,\kappa,\mu) =
+            \left({\frac{\\b}{\kappa + 1/\kappa}}\right)\,e^{-(x-\mu)\\b\,s\kappa ^{s}}}
 
     where
 
     .. math::
 
-        s = sgn(x)
+        s = sgn(x-\mu)
 
     ========  ========================
     Support   :math:`x \in \mathbb{R}`
@@ -1706,13 +1706,16 @@ def __init__(self, b, kappa, mu=0, *args, **kwargs):
         self.mean = self.mu - (self.kappa - 1 / self.kappa) / b
         self.variance = (1 + self.kappa ** 4) / (self.kappa ** 2 * self.b ** 2)
 
+        assert_negative_support(kappa, "kappa", "AsymmetricLaplace")
+        assert_negative_support(b, "b", "AsymmetricLaplace")
+
         super().__init__(*args, **kwargs)
 
-    def _random(self, b, kappa, size=None):
+    def _random(self, b, kappa, mu, size=None):
         u = np.random.uniform(size=size)
         switch = kappa ** 2 / (1 + kappa ** 2)
-        non_positive_x = kappa * np.log(u * (1 / switch)) / b
-        positive_x = -np.log((1 - u) * (1 + kappa ** 2)) / (kappa * b)
+        non_positive_x = mu + kappa * np.log(u * (1 / switch)) / b
+        positive_x = mu - np.log((1 - u) * (1 + kappa ** 2)) / (kappa * b)
         draws = non_positive_x * (u <= switch) + positive_x * (u > switch)
         return draws
 
@@ -1733,8 +1736,8 @@ def random(self, point=None, size=None):
         -------
         array
         """
-        b, kappa = draw_values([self.b, self.kappa], point=point, size=size)
-        return generate_samples(self._random, b, kappa, dist_shape=self.shape, size=size)
+        b, kappa, mu = draw_values([self.b, self.kappa, self.mu], point=point, size=size)
+        return generate_samples(self._random, b, kappa, mu, dist_shape=self.shape, size=size)
 
     def logp(self, value):
         """
diff --git a/pymc3/tests/test_distributions.py b/pymc3/tests/test_distributions.py
index 7f7e1195e9..c2548423f6 100644
--- a/pymc3/tests/test_distributions.py
+++ b/pymc3/tests/test_distributions.py
@@ -220,8 +220,9 @@ def build_model(distfam, valuedomain, vardomains, extra_args=None):
     return m
 
 
-def laplace_asymmetric_logpdf(value, kappa, b):
+def laplace_asymmetric_logpdf(value, kappa, b, mu):
     kapinv = 1 / kappa
+    value = value - mu
     lPx = value * b * np.where(value >= 0, -kappa, kapinv)
     lPx += np.log(b / (kappa + kapinv))
     return lPx
@@ -999,7 +1000,7 @@ def test_laplace_asymmetric(self):
         self.pymc3_matches_scipy(
             AsymmetricLaplace,
             R,
-            {"b": Rplus, "kappa": Rplus},
+            {"b": Rplus, "kappa": Rplus, "mu": R},
             laplace_asymmetric_logpdf,
         )
 
diff --git a/pymc3/tests/test_distributions_random.py b/pymc3/tests/test_distributions_random.py
index 19b7901f8e..6cc4fe8042 100644
--- a/pymc3/tests/test_distributions_random.py
+++ b/pymc3/tests/test_distributions_random.py
@@ -377,7 +377,7 @@ class TestLaplace(BaseTestCases.BaseTestCase):
 
 class TestAsymmetricLaplace(BaseTestCases.BaseTestCase):
     distribution = pm.AsymmetricLaplace
-    params = {"kappa": 1.0, "b": 1.0}
+    params = {"kappa": 1.0, "b": 1.0, "mu": 0.0}
 
 
 class TestLognormal(BaseTestCases.BaseTestCase):
@@ -632,17 +632,15 @@ def ref_rand(size, mu, b):
         pymc3_random(pm.Laplace, {"mu": R, "b": Rplus}, ref_rand=ref_rand)
 
     def test_laplace_asymmetric(self):
-        def ref_rand(size, kappa, b):
+        def ref_rand(size, kappa, b, mu):
             u = np.random.uniform(size=size)
-            x = -np.log((1 - u) * (1 + kappa ** 2)) / (kappa * b) * (
-                u > ((kappa ** 2) / (1 + kappa ** 2))
-            ) + kappa * np.log(u * (1 + kappa ** 2) / (kappa ** 2)) / b * (
-                u < ((kappa ** 2) / (1 + kappa ** 2))
-            )
-
-            return x
+            switch = kappa ** 2 / (1 + kappa ** 2)
+            non_positive_x = mu + kappa * np.log(u * (1 / switch)) / b
+            positive_x = mu - np.log((1 - u) * (1 + kappa ** 2)) / (kappa * b)
+            draws = non_positive_x * (u <= switch) + positive_x * (u > switch)
+            return draws
 
-        pymc3_random(pm.AsymmetricLaplace, {"b": Rplus, "kappa": Rplus}, ref_rand=ref_rand)
+        pymc3_random(pm.AsymmetricLaplace, {"b": Rplus, "kappa": Rplus, "mu": R}, ref_rand=ref_rand)
 
     def test_lognormal(self):
         def ref_rand(size, mu, tau):