Implement icdf() method for Asymmetric Laplace distribution and provide corresponding tests, as requested in issue #6612.

Author: darmendariz

pymc/distributions/continuous.py

@@ -1640,6 +1640,15 @@ def logp(value, b, kappa, mu):
             msg="b > 0, kappa > 0",
         )
 
+    def icdf(value, b, kappa, mu):
+        res = pt.switch(
+            pt.le(value, kappa**2 / (1 + kappa**2)),
+            mu + (kappa / b) * pt.log(value * (1 + kappa**2) / kappa**2),
+            mu - (1 / (b * kappa)) * pt.log((1 - value) * (1 + kappa**2)),
+        )
+        res = check_icdf_value(res, value)
+        return check_icdf_parameters(res, b > 0, kappa > 0, msg="b > 0, kappa > 0")
+
 
 class LogNormal(PositiveContinuous):
     r"""

tests/distributions/test_continuous.py

@@ -489,6 +489,12 @@ def test_laplace_asymmetric(self):
             laplace_asymmetric_logpdf,
             decimal=select_by_precision(float64=6, float32=2),
         )
+        check_icdf(
+            pm.AsymmetricLaplace,
+            {"b": Rplus, "kappa": Rplus, "mu": R},
+            # scipy uses an alternative scale parameterization, scale=1/b
+            lambda q, b, kappa, mu: st.laplace_asymmetric.ppf(q, kappa, mu, 1 / b),
+        )
 
     def test_lognormal(self):
         check_logp(