Dimensionality reduction techniques are essential in modern data analysis to enable interpretable representations of high-dimensional data. Principal component analysis (PCA), a widespread approach, identifies directions of maximal variance and provides linear projections, but does not account for uncertainty in the data. The recently proposed uncertainty-aware PCA (UAPCA) extends PCA by modeling each data point not as a fixed vector but as a probability distribution, focusing on multivariate normal distributed data. However, many real-world datasets exhibit non-normal characteristics, rendering the Gaussian assumption insufficient. This thesis introduces a generalization termed non-normal uncertainty-aware PCA (NNUAPCA), that projects arbitrary probability density functions, such as Gaussian mixture models or histograms, into lower-dimensional spaces while preserving the uncertainty structure introduced by UAPCA. By analytically propagating non-Gaussian uncertainty through the DR pipeline, NNUAPCAovercomes the limitations ofUAPCA and makes our approach more applicable and accurate. The method is evaluated on synthetic and real-world datasets using qualitative visualizations and quantitative measures. Empirical results demonstrate that NNUAPCA produces low-dimensional embeddings that more faithfully preserve the uncertain structure of non-normally distributed data, while maintaining lower computational cost compared to other approaches.