Add ICDF function to pareto distribution

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

Issue pymc-devs#6612

pymc/distributions/continuous.py

@@ -1943,6 +1943,16 @@ 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

@@ -638,6 +638,11 @@ 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"),