Sequencing of the T cell receptor (TCR) repertoire is a powerful tool for deeper study of immune response, but the unique structure of this type of data makes its meaningful quantification challenging. We introduce a new method, the Gamma-GPD spliced threshold model, to address this difficulty. This biologically interpretable model captures the distribution of the TCR repertoire, demonstrates stability across varying sequencing depths, and permits comparative analysis across any number of sampled individuals. We apply our method to several datasets and obtain insights regarding the differentiating features in the T cell receptor repertoire among sampled individuals across conditions. We have implemented our method in the open-source R package powerTCR.