In this paper, we introduce the kernel cumulative density estimator (KCDE): a novel, data-driven, kernel-based approach to conduct Gaussian anamorphosis. We use a non-parametric kernel-smoothing procedure based on the data’s cumulative density function (CDF) to estimate \({\hat{F}_{\textrm{KCDE}}}\) . This smooth, injective, monotonic kernel-based function efficiently transforms the CDF to a normal distribution. The inverse transformation back to the original scale of the values can be achieved through a lookup table (LUT). The flexibility and accuracy of KCDE are demonstrated on two datasets: a univariate zinc concentration dataset, where it addresses skewed, non-Gaussian behaviors with several negative values, and a multivariate geochemistry dataset of aluminum and zinc concentrations with several zero values. In both cases, the KCDE reliably transforms the variables to a normal distribution, enabling the investigation of prediction uncertainty via the kriging error variable or statistical simulations. The multivariate dataset is utilized to perform Monte Carlo conditional simulations to showcase the applicability of the method.
