This paper introduces a distributionally robust optimization (DRO) framework under moment uncertainty, applicable to data-driven problems. The model accounts for uncertainty in both the form of the distribution (e.g., discrete, Gaussian, exponential) and its moments (mean and covariance). It demonstrates that for a wide range of cost functions, the associated DRO stochastic program can be solved efficiently. By deriving new confidence regions for the mean and covariance of a random vector, the paper provides probabilistic arguments for using the model in problems relying on historical data. This is validated through a portfolio selection example, where the framework leads to better performance on the true distribution of asset returns. The paper addresses the computational challenges of solving stochastic programs, which often require strong assumptions about the distribution of random parameters. The proposed DRO model relaxes these assumptions by considering uncertainty in the distribution's form and moments. It introduces a distributional set that accounts for moment uncertainty, allowing for more accurate modeling of distributional uncertainty in data-driven problems. The paper shows that under certain assumptions, the DRO model can be solved in polynomial time for a wide range of optimization problems. It also derives a new form of confidence region for the mean and covariance of a random vector, which naturally leads to using the proposed distributional set. These results demonstrate that the distributional set is suitable for data-driven problems where knowledge of the random variables is derived from historical data. The paper applies the framework to a portfolio selection problem, demonstrating that the model performs better on the true distribution of asset returns compared to previously proposed DRO formulations. The results show that the model not only offers computational advantages but also performs well in practice. The paper concludes that the proposed distributional set is a robust and tractable framework for distributional uncertainty in data-driven problems.This paper introduces a distributionally robust optimization (DRO) framework under moment uncertainty, applicable to data-driven problems. The model accounts for uncertainty in both the form of the distribution (e.g., discrete, Gaussian, exponential) and its moments (mean and covariance). It demonstrates that for a wide range of cost functions, the associated DRO stochastic program can be solved efficiently. By deriving new confidence regions for the mean and covariance of a random vector, the paper provides probabilistic arguments for using the model in problems relying on historical data. This is validated through a portfolio selection example, where the framework leads to better performance on the true distribution of asset returns. The paper addresses the computational challenges of solving stochastic programs, which often require strong assumptions about the distribution of random parameters. The proposed DRO model relaxes these assumptions by considering uncertainty in the distribution's form and moments. It introduces a distributional set that accounts for moment uncertainty, allowing for more accurate modeling of distributional uncertainty in data-driven problems. The paper shows that under certain assumptions, the DRO model can be solved in polynomial time for a wide range of optimization problems. It also derives a new form of confidence region for the mean and covariance of a random vector, which naturally leads to using the proposed distributional set. These results demonstrate that the distributional set is suitable for data-driven problems where knowledge of the random variables is derived from historical data. The paper applies the framework to a portfolio selection problem, demonstrating that the model performs better on the true distribution of asset returns compared to previously proposed DRO formulations. The results show that the model not only offers computational advantages but also performs well in practice. The paper concludes that the proposed distributional set is a robust and tractable framework for distributional uncertainty in data-driven problems.