LiDAR inertial odometry (LIO) has attracted much attention due to the complementarity of LiDAR and IMU measurements. In the distribution-based LIO, the components related to distribution covariance in the residual and residual uncertainty from the LiDAR measurement noise is neutralized. And the resultant point cloud constraint degeneration problem severely affects the accuracy of pose estimation. In this article, a hierarchical tightly-coupled LIO based on distribution is proposed. By excluding the eigenvalue elements in the distribution covariance component with the designed loss function, the uncertainty of corresponding residual is rectified.As a result, the degeneration problem is solved.With anti-degeneration point-to-distribution constraints, a LiDAR inertial odometry based on iterated extended Kalman filter and a factor graph optimization are designed and organized in a hierarchical way to achieve coarse-to-fine pose estimation, where LiDAR and IMU measurements are tightly coupled in both layers. In this way, the respective advantages of high efficiency and high accuracy from filtering and optimization are combined, which offers high-fidelity estimation results in real time. The effectiveness of the proposed method is verified through experiments on the public NC and ENC datasets.