On characterization of the Cauchy law by sample mean properties - Januškevičius, Romanas (Lietuvos matematikos rinkinys, 2004)
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