Add HalfStudent icdf

Author: dalai444

pymc/distributions/continuous.py

@@ -2834,6 +2834,13 @@ def logp(value, nu, sigma):
             msg="sigma > 0, nu > 0",
         )
 
+    def icdf(value, nu, sigma):
+        # Map half-t quantiles to full StudentT quantiles:
+        # F_half^{-1}(u) = F_t^{-1}((u + 1)/2; nu, mu=0, sigma)
+        res = icdf(StudentT.dist(nu, sigma=sigma), (value + 1.0) / 2.0)
+        res = check_icdf_value(res, value)
+        return res
+
 
 class ExGaussianRV(SymbolicRandomVariable):
     name = "exgaussian"

tests/distributions/test_continuous.py

@@ -575,6 +575,13 @@ def test_studentt_icdf(self):
             lambda q, nu, mu, sigma: st.t.ppf(q, nu, mu, sigma),
         )
 
+    def test_halfstudentt_icdf(self):
+        check_icdf(
+            pm.HalfStudentT,
+            {"nu": Rplusbig, "sigma": Rplusbig},
+            lambda q, nu, sigma: st.t.ppf(0.5 * (q + 1.0), nu, 0.0, sigma),
+        )
+
     @pytest.mark.skipif(
         condition=(pytensor.config.floatX == "float32"),
         reason="Fails on float32 due to numerical issues",