We investigate the statistical modeling of hyper-spectral data. The accurate modeling of experimental data is critical in target detection and classification applications. In fact, having a statistical model that is capable of properly describing data variability leads to the derivation of the best decision strategies together with a reliable assessment of algorithm performance. Most existing classification and target detection algorithms are based on the multivariate Gaussian model which, in many cases, deviates from the true statistical behavior of hyper-spectral data. This motivated us to investigate the capability of non-Gaussian models to represent data variability in each background class. In particular, we refer to models based on elliptically contoured (EC) distributions. We consider multivariate EC-t distribution and two distinct mixture models based on EC distributions. We describe the methodology adopted for the statistical analysis and we propose a technique to automatically estimate the unknown parameters of statistical models. Finally, we discuss the results obtained by analyzing data gathered by the multispectral infrared and visible imaging spectrometer (MIVIS) sensor.