This paper addresses the challenge of solving stochastic programs in uncertain environments, particularly when there is ambiguity in the choice of distribution for random parameters. The authors propose a distributionally robust optimization (DRO) model that accounts for both the form of the distribution (discrete, Gaussian, exponential, etc.) and its moments (mean and covariance). They demonstrate that for a wide range of cost functions, the associated DRO stochastic program can be solved efficiently. Additionally, they derive new confidence regions for the mean and covariance of a random vector, providing probabilistic arguments for using their model in data-driven problems. The practical effectiveness of their framework is demonstrated through a portfolio selection example, where their model outperforms previous DRO formulations in terms of performance on the true distribution underlying daily asset returns. The paper also discusses the computational complexity of solving the moment problem and the DRSP model under the proposed distributional set, showing that both can be solved in polynomial time. Finally, the authors explore the application of their framework to conditional value-at-risk (CVaR) and data-driven stochastic programming, providing theoretical guarantees for the robustness of the solutions.This paper addresses the challenge of solving stochastic programs in uncertain environments, particularly when there is ambiguity in the choice of distribution for random parameters. The authors propose a distributionally robust optimization (DRO) model that accounts for both the form of the distribution (discrete, Gaussian, exponential, etc.) and its moments (mean and covariance). They demonstrate that for a wide range of cost functions, the associated DRO stochastic program can be solved efficiently. Additionally, they derive new confidence regions for the mean and covariance of a random vector, providing probabilistic arguments for using their model in data-driven problems. The practical effectiveness of their framework is demonstrated through a portfolio selection example, where their model outperforms previous DRO formulations in terms of performance on the true distribution underlying daily asset returns. The paper also discusses the computational complexity of solving the moment problem and the DRSP model under the proposed distributional set, showing that both can be solved in polynomial time. Finally, the authors explore the application of their framework to conditional value-at-risk (CVaR) and data-driven stochastic programming, providing theoretical guarantees for the robustness of the solutions.