diff --git a/python/paddle/distribution/beta.py b/python/paddle/distribution/beta.py
index 8045be4b1fa923..f5bf8a13275f01 100644
--- a/python/paddle/distribution/beta.py
+++ b/python/paddle/distribution/beta.py
@@ -150,7 +150,7 @@ def sample(self, shape: Sequence[int] = ()) -> Tensor:
             shape (Sequence[int], optional): Sample shape.
 
         Returns:
-            Sampled data with shape `sample_shape` + `batch_shape` + `event_shape`.
+            Tensor, Sampled data with shape `sample_shape` + `batch_shape` + `event_shape`.
         """
         shape = shape if isinstance(shape, tuple) else tuple(shape)
         return paddle.squeeze(self._dirichlet.sample(shape)[..., 0], axis=-1)
diff --git a/python/paddle/distribution/lkj_cholesky.py b/python/paddle/distribution/lkj_cholesky.py
index fc2cb5c6c33e6f..b2dd807e709b26 100644
--- a/python/paddle/distribution/lkj_cholesky.py
+++ b/python/paddle/distribution/lkj_cholesky.py
@@ -11,11 +11,13 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+from __future__ import annotations
 
 import math
 import operator
 from collections.abc import Sequence
 from functools import reduce
+from typing import TYPE_CHECKING, Literal
 
 import paddle
 from paddle.base.data_feeder import check_type, convert_dtype
@@ -24,6 +26,11 @@
 from paddle.distribution.beta import Beta
 from paddle.framework import in_dynamic_mode
 
+if TYPE_CHECKING:
+    from paddle import Tensor
+    from paddle._typing import DTypeLike
+
+
 __all__ = ["LKJCholesky"]
 
 
@@ -95,7 +102,7 @@ def vec_to_tril_matrix(
     return matrix
 
 
-def tril_matrix_to_vec(mat: paddle.Tensor, diag: int = 0) -> paddle.Tensor:
+def tril_matrix_to_vec(mat: Tensor, diag: int = 0) -> Tensor:
     r"""
     Convert a `D x D` matrix or a batch of matrices into a (batched) vector
     which comprises of lower triangular elements from the matrix in row order.
@@ -139,7 +146,17 @@ class LKJCholesky(distribution.Distribution):
             [3, 3]
     """
 
-    def __init__(self, dim=2, concentration=1.0, sample_method="onion"):
+    concentration: Tensor
+    dtype: DTypeLike
+    dim: int
+    sample_method: Literal["onion", "cvine"]
+
+    def __init__(
+        self,
+        dim: int = 2,
+        concentration: float = 1.0,
+        sample_method: Literal["onion", "cvine"] = "onion",
+    ) -> None:
         if not in_dynamic_mode():
             check_type(
                 dim,
@@ -209,14 +226,14 @@ def __init__(self, dim=2, concentration=1.0, sample_method="onion"):
             raise ValueError("`method` should be one of 'cvine' or 'onion'.")
         super().__init__(batch_shape, event_shape)
 
-    def _onion(self, sample_shape):
+    def _onion(self, sample_shape: Sequence[int]) -> Tensor:
         """Generate a sample using the "onion" method.
 
         Args:
             sample_shape (tuple): The shape of the samples to be generated.
 
         Returns:
-            w (paddle.Tensor): The Cholesky factor of the sampled correlation matrix.
+            w (Tensor): The Cholesky factor of the sampled correlation matrix.
         """
         # Sample y from the Beta distribution
         y = self._beta.sample(sample_shape).unsqueeze(-1)
@@ -249,14 +266,14 @@ def _onion(self, sample_shape):
         w += paddle.diag_embed(diag_elems)
         return w
 
-    def _cvine(self, sample_shape):
+    def _cvine(self, sample_shape: Sequence[int]) -> Tensor:
         """Generate a sample using the "cvine" method.
 
         Args:
             sample_shape (tuple): The shape of the samples to be generated.
 
         Returns:
-            r (paddle.Tensor): The Cholesky factor of the sampled correlation matrix.
+            r (Tensor): The Cholesky factor of the sampled correlation matrix.
         """
 
         # Sample beta and calculate partial correlations
@@ -308,7 +325,7 @@ def _cvine(self, sample_shape):
             r = r.reshape((flatten_shape // last_dim, self.dim, self.dim))
         return r
 
-    def sample(self, sample_shape=()):
+    def sample(self, sample_shape: Sequence[int] = ()) -> Tensor:
         """Generate a sample using the specified sampling method."""
         if not isinstance(sample_shape, Sequence):
             raise TypeError('sample shape must be Sequence object.')
@@ -334,14 +351,14 @@ def sample(self, sample_shape=()):
 
         return res.reshape(output_shape)
 
-    def log_prob(self, value):
+    def log_prob(self, value: Tensor) -> Tensor:
         r"""Compute the log probability density of the given Cholesky factor under the LKJ distribution.
 
         Args:
-            value (paddle.Tensor): The Cholesky factor of the correlation matrix for which the log probability density is to be computed.
+            value (Tensor): The Cholesky factor of the correlation matrix for which the log probability density is to be computed.
 
         Returns:
-            log_prob (paddle.Tensor): The log probability density of the given Cholesky factor under the LKJ distribution.
+            log_prob (Tensor): The log probability density of the given Cholesky factor under the LKJ distribution.
         """
         # 1.Compute the order vector.
         diag_elems = paddle.diagonal(value, offset=0, axis1=-1, axis2=-2)[