Description: This paper critiques and supplements Professor Schuette's 'Linear Programming Approach to Graduation.' The main points are: 1. The graduation is a problem of estimating the mean vector of a multivariate variable under certain assumptions. Schuette and other discussants emphasized the robustness property of their proposed estimation. This paper points out their mistake and suggests some correcting directions based on Bayesian theory. 2. This paper provides a more complete theoretical rationale for the parameter choosing in the graduation problem. 3. This paper points out the incompleteness of a theorem's proof in Schuette's paper and supplements some interpretations and mathematical details for the proof of some other theorems from a different viewpoint.

Description: A statistical estimate is obtained for the total number of nodes in a three level tree. The number of nodes at each level is randomly distributed with certain pattern of distribution. Then the result is applied to the problem of estimating the LRA [logical record access] in data base design in a more refined way. It is more refined in the sense of using more information contained in the empirical distributions and being associated with a probability statement.

Description: This paper suggests that a mixture of pay-as-you-go and reserve financing would help Taiwan's troubled social security program. From Actuarial Research Clearing House 2009, Vol 2.