Single-cell transcriptomic data approximates the abundance of proteins at a high resolution, but its noisiness necessitates transformation by a pipeline of methods before analysis and inference. In the absence of robust validation of these pipelines and methods, it remains unclear how best to process any particular dataset. To compensate for this, popular visualisation methods, e.g., t-SNE and UMAP, are commonly used to produce descriptions of datasets. Such visualisations are incomplete and provide subjective descriptions of samples rather than statistically meaningful statements about technical noise or biology. In this paper, we introduce the Zero-Inflated Negative-Binomial with Geometric Tail (ZINBGT), a mixture-model-based strategy for producing interpretable visualisations of each gene's expression across cells, along with diagnostic summaries that use Wasserstein distance to highlight outlier genes. These diagnostics are used to reveal an outlier gene within a T. brucei sample. This method is applied to a human immune-cell dataset, highlighting the relationship between sparsity, mean, and spread across genes, as well as revealing an issue with the use of zero-inflated negative-binomial distributions to model single-cell RNA data. An investigation of simulated datasets intended to replicate the immune-cell data revealed discrepancies with the ground truth, establishing purposes for which these simulated datasets are unsuitable. Finally, we list a number of different domains to which this method can be applied.

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