Independent Linear Statistics on Finite Abelian Groups

  • P. Graczyk
  • G. M. Fel'dman


We give a complete description of the class of all finite Abelian groups X for which the independence of linear statistics L 1 = α11) + α22) + α33) and L 2 = β11) + β22) + β33) (here, ξ j , j = 1, 2, 3, are independent random variables with values in X and distributions μ j ; α j and β j are automorphisms of X) implies that either one, or two, or three of the distributions μ j are idempotents.
How to Cite
Graczyk, P., and G. M. Fel’dman. “Independent Linear Statistics on Finite Abelian Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 4, Apr. 2001, pp. 441-8,
Research articles