The characteristic function of the discrete Cauchy distribution

Abstract

A new family of integer-valued Cauchy-type distributions is introduced, the {\it Cauchy-Cacoullos family}. The characteristic function is evaluated, showing some interesting distributional properties, similar to the ordinary (continuous) Cauchy scale family. The results are extendable to discrete Student-type distributions with odd degrees of freedom. Keywords: Fourier series; discrete Student distribution; Cauchy-Cacoullos family.Comment: Dedicated to Professor Theo Cacoullos (13 pages, 1 Figure