In many real-world scenarios, like quantitative finance, datasets exhibit a probability distribution with significant skewness. Neglecting fat-tails can lead to increased estimation errors and potential business losses. We introduce a new classifier, termed Elliptical Discriminant, that generalise Quadratic Discriminant Analysis (QDA) to handle fat-tailed data. This is demonstrated using a multivariate dataset with fat-tails and a comparative study with other well-known classifiers.