In this paper, we deal with the problem of database statistics publishing with privacy and utility guarantees. While various privacy and utility metrics have been proposed, purposes of using the statistics for a user and an adversary and their background knowledge about the database have not been specified. We model the user and the adversary from two perspectives. First, we model their background knowledge: knowledge of statistics of the database and knowledge of distribution for the database. Then we model the purposes of them as decision functions in statistical decision theory. Privacy and utility metrics are defined based on risk functions. Comparison of the statistical decision-theoretic framework we propose and differential privacy framework is made through a numerical example.