Literature cited
G. Darmois, “Analyse generale des liaisons stochastiques,” Rev. Inst. Intern. Stat.,21, 2–8 (1953).
V. P. Skitovich, “Linear forms of independent random variables and the normal distribution,” Izv. Akad. Nauk SSSR, Ser. Math.,18, No. 2, 185–200 (1954).
R. G. Laha, “On a characterization of the normal distribution from properties of suitable linear statistics,” Ann. Math. Stat.,27, No. 1, 126–139 (1956).
A. A. Zinger and A. M. Kagan, “Toward analytical theory of linear forms of independent random variables,” J. Sov. Math.,44, No. 4 (1989).
J. Marcinkiewicz, “Sur une propriete de la loi de Gauss,” Math. Z.,44, 632–638 (1938).
Yu. V. Linnik and I. V. Ostrovskii, Decomposition of Random Variables and Vectors [in Russian], Nauka, Moscow (1972).
Yu. V. Linnik, “Linear forms and statistical tests. I, II,” Ukr. Mat. Zh.,5, No. 2, 207–243, NO. 3, 247–290 (1953).
A. M. Kagan, Yu. V. Linnik, and S. R. Rao, Characterization Problems of Mathematical Statistics [in Russian], Nauka, Moscow (1972).
Additional information
Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, pp. 40–45, 1987.
Rights and permissions
About this article
Cite this article
Zinger, A.A., Kagan, A.M. Condition of constancy of the regression for monomials of independent random variables. J Math Sci 47, 2708–2713 (1989). https://doi.org/10.1007/BF01095596
Issue Date:
DOI: https://doi.org/10.1007/BF01095596