A new approximation for the distribution of the difference of two t-variables

A mixture representation for the distribution of the difference of two independent t-varlables is provided to approximate the probabilities and percentiles The mixture of normal and standardized t is found to be quite suitable in terms of the accuracy and simplicity as it compares favorably to the best known approximation namelyt that due to Ghosh (1975). The idea of the mixture distribution is also extended to provide an approximation to the distribution of a linear combination of independent t-variables which provides an approximation to the Behrens-Fisher distribution in particular.