diff --git a/mindspore/nn/probability/distribution/_utils/utils.py b/mindspore/nn/probability/distribution/_utils/utils.py
index 58d1c7cd014..e4fd79154ec 100644
--- a/mindspore/nn/probability/distribution/_utils/utils.py
+++ b/mindspore/nn/probability/distribution/_utils/utils.py
@@ -272,6 +272,10 @@ def check_type(data_type, value_type, name):
 def raise_none_error(name):
     raise ValueError(f"{name} should be specified. Value cannot be None")
 
+@constexpr
+def raise_not_impl_error(name):
+    raise ValueError(f"{name} function should be implemented for non-linear transformation")
+
 @constexpr
 def check_distribution_name(name, expected_name):
     if name != expected_name:
diff --git a/mindspore/nn/probability/distribution/transformed_distribution.py b/mindspore/nn/probability/distribution/transformed_distribution.py
index baed5f10d13..259f105d4e8 100644
--- a/mindspore/nn/probability/distribution/transformed_distribution.py
+++ b/mindspore/nn/probability/distribution/transformed_distribution.py
@@ -18,7 +18,7 @@ from mindspore._checkparam import Validator as validator
 from mindspore.common import dtype as mstype
 import mindspore.nn as nn
 from .distribution import Distribution
-from ._utils.utils import check_type
+from ._utils.utils import check_type, raise_not_impl_error
 
 class TransformedDistribution(Distribution):
     """
@@ -56,6 +56,7 @@ class TransformedDistribution(Distribution):
         self._distribution = distribution
         self._is_linear_transformation = bijector.is_constant_jacobian
         self.exp = P.Exp()
+        self.log = P.Log()
 
     @property
     def bijector(self):
@@ -69,37 +70,49 @@ class TransformedDistribution(Distribution):
     def is_linear_transformation(self):
         return self._is_linear_transformation
 
-    def _cdf(self, value):
+    def _cdf(self, *args, **kwargs):
         r"""
         .. math::
             Y = g(X)
             P(Y <= a) = P(X <= g^{-1}(a))
         """
-        inverse_value = self.bijector.inverse(value)
-        return self.distribution.cdf(inverse_value)
+        inverse_value = self.bijector("inverse", *args, **kwargs)
+        return self.distribution("cdf", inverse_value)
 
-    def _log_prob(self, value):
+    def _log_cdf(self, *args, **kwargs):
+        return self.log(self._cdf(*args, **kwargs))
+
+    def _survival_function(self, *args, **kwargs):
+        return 1.0 - self._cdf(*args, **kwargs)
+
+    def _log_survival(self, *args, **kwargs):
+        return self.log(self._survival_function(*args, **kwargs))
+
+    def _log_prob(self, *args, **kwargs):
         r"""
         .. math::
             Y = g(X)
             Py(a) = Px(g^{-1}(a)) * (g^{-1})'(a)
             \log(Py(a)) = \log(Px(g^{-1}(a))) + \log((g^{-1})'(a))
         """
-        inverse_value = self.bijector.inverse(value)
-        unadjust_prob = self.distribution.log_prob(inverse_value)
-        log_jacobian = self.bijector.inverse_log_jacobian(value)
+        inverse_value = self.bijector("inverse", *args, **kwargs)
+        unadjust_prob = self.distribution("log_prob", inverse_value)
+        log_jacobian = self.bijector("inverse_log_jacobian", *args, **kwargs)
         return unadjust_prob + log_jacobian
 
-    def _prob(self, value):
-        return self.exp(self._log_prob(value))
+    def _prob(self, *args, **kwargs):
+        return self.exp(self._log_prob(*args, **kwargs))
 
-    def _sample(self, shape):
-        org_sample = self.distribution.sample(shape)
-        return self.bijector.forward(org_sample)
+    def _sample(self, *args, **kwargs):
+        org_sample = self.distribution("sample", shape)
+        return self.bijector("forward", org_sample)
 
-    def _mean(self):
+    def _mean(self, *args, **kwargs):
         """
         Note:
             This function maybe overridden by derived class.
         """
-        return self.bijector.forward(self.distribution.mean())
+        if not self.is_linear_transformation:
+            raise_not_impl_error(mean)
+
+        return self.bijector("forward", self.distribution("mean"))