The statistical methods for the financial returns play a key role in measuring the goodness-of-fit of a given distribution to real data. As is well known, the normal inverse Gaussian (NIG) and generalized hyperbolic skew-t (GHST) distributions have been found to successfully describe the data of the returns from financial market. In this paper, we mainly consider the discrimination between these distributions. It is observed that the maximum likelihood estimators (MLEs) cannot be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators. The approximate confidence intervals of the unknown parameters have been constructed. We then perform a number of goodness-of-fit tests to compare the NIG and GHST distributions for the stock exchange data. Moreover, the Vuong type test, based on the Kullback-Leibler information criteria, has been considered to select the most appropriate candidate model. An important implication of the present study is that the GHST distribution function, in contrast to NIG distribution, may describe more appropriate for the proposed data.