Add ICDF for the Kumaraswamy distribution (#6642)

* Added ICDF for the Kumaraswamy distribution.

* Added icdf - logcdf consistency tests.

* Tmp testing with np assert_almost_equal print messages.

* Testing a fix by truncating cdf to precision.

* Revert "Tmp testing with np assert_almost_equal print messages."

This reverts commit b0c93b77e3d39c81b22325b644cf94c2beeb9e9c.

Avoid mypy test failure. This is not needed, we have identified
the root cause now.

* Remove discrete selfconsistency icdf

---------

Co-authored-by: Ricardo Vieira <ricardo.vieira1994@gmail.com>

Author: gokuld

pymc/distributions/continuous.py

@@ -1324,6 +1324,16 @@ def logcdf(value, a, b):
             msg="a > 0, b > 0",
         )
 
+    def icdf(value, a, b):
+        res = pt.exp(pt.reciprocal(a) * pt.log1mexp(pt.reciprocal(b) * pt.log1p(-value)))
+        res = check_icdf_value(res, value)
+        return check_icdf_parameters(
+            res,
+            a > 0,
+            b > 0,
+            msg="a > 0, b > 0",
+        )
+
 
 class Exponential(PositiveContinuous):
     r"""

pymc/testing.py

@@ -668,6 +668,52 @@ def check_selfconsistency_discrete_logcdf(
             )
 
 
+def check_selfconsistency_icdf(
+    distribution: Distribution,
+    paramdomains: dict[str, Domain],
+    *,
+    decimal: int | None = None,
+    n_samples: int = 100,
+) -> None:
+    """Check that the icdf and logcdf functions of the distribution are consistent.
+
+    Only works with continuous distributions.
+    """
+    if decimal is None:
+        decimal = select_by_precision(float64=6, float32=3)
+
+    dist = create_dist_from_paramdomains(distribution, paramdomains)
+    if dist.type.dtype.startswith("int"):
+        raise NotImplementedError(
+            "check_selfconsistency_icdf is not robust against discrete distributions."
+        )
+    value = dist.astype("float64").type("value")
+    dist_icdf = icdf(dist, value)
+    dist_cdf = pt.exp(logcdf(dist, value))
+
+    py_mode = Mode("py")
+    dist_icdf_fn = pytensor.function(list(inputvars(dist_icdf)), dist_icdf, mode=py_mode)
+    dist_cdf_fn = compile(list(inputvars(dist_cdf)), dist_cdf, mode=py_mode)
+
+    domains = paramdomains.copy()
+    domains["value"] = Domain(np.linspace(0, 1, 10))
+
+    for point in product(domains, n_samples=n_samples):
+        point = dict(point)
+        value = point.pop("value")
+        icdf_value = dist_icdf_fn(**point, value=value)
+        recovered_value = dist_cdf_fn(
+            **point,
+            value=icdf_value,
+        )
+        np.testing.assert_almost_equal(
+            value,
+            recovered_value,
+            decimal=decimal,
+            err_msg=f"point: {point}",
+        )
+
+
 def assert_support_point_is_expected(model, expected, check_finite_logp=True):
     fn = make_initial_point_fn(
         model=model,

tests/distributions/test_continuous.py

@@ -45,6 +45,7 @@
     check_icdf,
     check_logcdf,
     check_logp,
+    check_selfconsistency_icdf,
     continuous_random_tester,
     seeded_numpy_distribution_builder,
     seeded_scipy_distribution_builder,
@@ -441,6 +442,10 @@ def scipy_log_cdf(value, a, b):
             {"a": Rplus, "b": Rplus},
             scipy_log_cdf,
         )
+        check_selfconsistency_icdf(
+            pm.Kumaraswamy,
+            {"a": Rplusbig, "b": Rplusbig},
+        )
 
     def test_exponential(self):
         check_logp(