Providing access to synthetic micro-data in place of confidential data to protect the privacy of participants is common practice. For the synthetic data to be useful for analysis, it is necessary that the density function of the synthetic data closely approximate the confidential data. Hence, accurately estimating the density function based on sample micro-data is important. Existing kernel-based, copula-based, and machine learning methods of joint density estimation may not be viable. Applying the multivariate moments’ problem to sample-based density estimation has long been considered impractical due to the computational complexity and intractability of optimal parameter selection of the density estimate when the true joint density function is unknown. This paper introduces a generalised form of the sample moment-based density estimate, which can be used to estimate joint density functions when only the information of empirical moments is available. We demonstrate optimal parametri