Random matrices find many applications in Physics and beyond. The ensembles used to compare with empirical covariance matrices carry the name of Wishart, Laguerre or chiral ensemble. We will generalise these standard ensembles introducing a one-parameter deformation that leads to power-law tails in the spectrum. After briefly reviewing other approaches we present our calculations\
based on orthogonal polynomials and an integral transform of the standard ensembles. This allows to keep full control of the limit of large NxM matrices, and we present a generalisation of the Marchenko-Pastur and Bessel distributions. We illustrate our results by comparing to time series in financial data, achieving an excellent agreement.