Add ICDF function to pareto distribution

Adds ICDF (quantile) function for the Pareto distribution. Source https://en.wikipedia.org/wiki/Pareto_distribution

Issue #6612

Author: james-2001

pymc/distributions/continuous.py

@@ -1482,16 +1482,10 @@ def logcdf(value, mu, b):
 
     def icdf(value, mu, b):
         res = pt.switch(
-            pt.le(value, 0.5),
-            mu + b * np.log(2 * value),
-            mu - b * np.log(2 - 2 * value)
+            pt.le(value, 0.5), mu + b * np.log(2 * value), mu - b * np.log(2 - 2 * value)
         )
         res = check_icdf_value(res, value)
-        return check_icdf_parameters(
-            res,
-            b > 0,
-            msg="b > 0"
-        )
+        return check_icdf_parameters(res, b > 0, msg="b > 0")
 
 
 class AsymmetricLaplaceRV(RandomVariable):
@@ -1943,6 +1937,16 @@ def logcdf(value, alpha, m):
             msg="alpha > 0, m > 0",
         )
 
+    def icdf(value, alpha, m):
+        res = m * pt.pow(1 - value, -1 / alpha)
+        res = check_icdf_value(res, value)
+        return check_icdf_parameters(
+            res,
+            alpha > 0,
+            m > 0,
+            msg="alpha > 0, m > 0",
+        )
+
 
 @_default_transform.register(Pareto)
 def pareto_default_transform(op, rv):

tests/distributions/test_continuous.py

@@ -457,11 +457,7 @@ def test_laplace(self):
             {"mu": R, "b": Rplus},
             lambda value, mu, b: st.laplace.logcdf(value, mu, b),
         )
-        check_icdf(
-            pm.Laplace,
-            {"mu": R, "b": Rplus},
-            lambda q, mu, b: st.laplace.ppf(q, mu, b)
-        )
+        check_icdf(pm.Laplace, {"mu": R, "b": Rplus}, lambda q, mu, b: st.laplace.ppf(q, mu, b))
 
     def test_laplace_asymmetric(self):
         check_logp(
@@ -638,6 +634,11 @@ def test_pareto(self):
             {"alpha": Rplusbig, "m": Rplusbig},
             lambda value, alpha, m: st.pareto.logcdf(value, alpha, scale=m),
         )
+        check_icdf(
+            pm.Pareto,
+            {"alpha": Rplusbig, "m": Rplusbig},
+            lambda q, alpha, m: st.pareto.ppf(q, alpha, scale=m),
+        )
 
     @pytest.mark.skipif(
         condition=(pytensor.config.floatX == "float32"),