Characterization of the Generalized Cauchy q-Distribution

This paper introduces a generalized q-Cauchy distribution built using the tools of qcalculus. We establish its main probabilistic properties, including its q-distribution function and q-moments. We also provide a characterization of this q-distribution based on a q-change-of-variable argument, showing how the model behaves under q-scaling and qsymmetry. These results offer a clear and accessible contribution to the study of q-deformed probability models. MSC 2020: 60E05, 62E10.