On characterization of the Cauchy law by sample mean properties

Abstract

The characterization of Cauchy distribution by assuming the identical distribution of a monomial and sample mean has been considered by B. Ramachandran, C.R. Rao, Y.H. Wang and other authors. The new proofs of Ramachandran-Rao and Wang's theorem are proposed in our paper.

Keywords

• characterization theorems
• stability theorems
• Cauchy distribution