Many signal and image processing applications are based on the classification of covariance matrices. These latter are elements on a Riemannian manifold for which many generative models have been developed in the literature. Recently, the Riemannian Laplace distribution (RLD) has been proposed to model the within-class variability of images. In this context, the present paper proposes an application of RLDs to the definition of Riemannian Fisher vectors issued from this Laplacian model. The expression of these descriptors is derived for mixtures of RLDs and their relation with the Riemannian vectors of locally aggregated descriptors is shown. Some comparisons with the bag of Riemannian words model are also performed. All these aforementioned descriptors are applied to texture image classification to find the most discriminating one. Moreover, to determine the best model for fitting the data, the classification performances are compared to those given by the Riemannian Gaussian distribution.