Implement icdf for Univariate distribution

pymc/distributions/continuous.py

@@ -343,6 +343,9 @@ def logcdf(value, lower, upper):
             msg="lower <= upper",
         )
 
+    def icdf(value, lower, upper):
+        return lower + (upper - lower) * value
+
 
 @_default_transform.register(Uniform)
 def uniform_default_transform(op, rv):
@@ -835,6 +838,9 @@ def logcdf(value, loc, sigma):
             msg="sigma > 0",
         )
 
+    def icdf(value, lower, upper, loc, sigma):
+        return stats.truncnorm.ppf(q=value, a=lower, b=upper, loc=loc, scale=sigma)
+
 
 class WaldRV(RandomVariable):
     name = "wald"
@@ -1013,6 +1019,42 @@ def logcdf(value, mu, lam, alpha):
             msg="mu > 0, lam > 0, alpha >= 0",
         )
 
+    def icdf(value, mu, lam, alpha=0):
+        """Calculate the inverse cumulative distribution function (icdf) of the Wald distribution.
+
+        Args
+        ----
+            value (float): Probability value between 0 and 1.
+            mu (float): Mean of the distribution.
+            lam (float): Scale of the distribution.
+
+        Returns
+        -------
+            float: The value x such that P(W <= x) = p, where W is the Wald distribution with given mu and lam.
+
+        Raises
+        ------
+            ValueError: If value is not between 0 and 1.
+            ValueError: If lam is not positive.
+        """
+        # Compute standard deviation and location parameter
+        std = at.sqrt(lam)
+        loc = alpha + mu
+
+        # Compute inverse standard normal CDF
+        z = at.sqrt(2) * at.erfinv(2 * value - 1)
+
+        # Compute Wald ICDF
+        x = loc + std * z / (1 - 0.5 * std * z)
+
+        return check_parameters(
+            x,
+            0 <= value <= 1,
+            lam > 0,
+            alpha >= 0,
+            msg="0<=val<=1, lam > 0, alpha >= 0",
+        )
+
 
 class BetaClippedRV(BetaRV):
     @classmethod

pymc/tests/distributions/test_continuous.py

@@ -26,7 +26,14 @@
 
 import pymc as pm
 
-from pymc.distributions.continuous import Normal, get_tau_sigma, interpolated
+from pymc.distributions.continuous import (
+    Normal,
+    TruncatedNormal,
+    Uniform,
+    Wald,
+    get_tau_sigma,
+    interpolated,
+)
 from pymc.distributions.dist_math import clipped_beta_rvs
 from pymc.logprob.abstract import logcdf
 from pymc.logprob.joint_logprob import logp
@@ -2281,5 +2288,25 @@ def test_normal_icdf(self, dist_params, obs, size):
         dist_params = dict(zip(dist_params_at, dist_params))
 
         x = Normal.dist(*dist_params_at, size=size_at)
-
         scipy_logprob_tester(x, obs, dist_params, test_fn=st.norm.ppf, test="icdf")
+
+    def test_uniform_icdf(self, dist_params, obs, size):
+        dist_params_at, obs_at, size_at = create_pytensor_params(dist_params, obs, size)
+        dist_params = dict(zip(dist_params_at, dist_params))
+
+        x = Uniform.dist(*dist_params_at, size=size_at)
+        scipy_logprob_tester(x, obs, dist_params, test_fn=st.uniform.ppf, test="icdf")
+
+    def test_truncated_normal_icdf(self, dist_params, obs, size):
+        dist_params_at, obs_at, size_at = create_pytensor_params(dist_params, obs, size)
+        dist_params = dict(zip(dist_params_at, dist_params))
+
+        x = TruncatedNormal.dist(*dist_params_at, size=size_at)
+        scipy_logprob_tester(x, obs, dist_params, test_fn=st.truncnorm.ppf, test="icdf")
+
+    def test_wald_icdf(self, *dist_params, obs, size):
+        dist_params_at, obs_at, size_at = create_pytensor_params(dist_params, obs, size)
+        dist_params = dict(zip(dist_params_at, dist_params))
+
+        x = Wald.dist(*dist_params_at, size=size_at)
+        scipy_logprob_tester(x, obs, dist_params, test_fn=st.wald.ppf, test="icdf")