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Literature cited
T. Kawata and H. Sakamoto, “On the characterization of the normal population by the independence of the sample mean and the sample variance,” J. Math. Soc. Jpn.,1, 111–115 (1949).
A. A. Zinger, “On independent samples from a normal population,” Usp. Mat. Nauk,6, No. 5, 172–175 (1951).
A. M. Mathai and G. Pederzoli, Characterizations of the Normal Probability Law, Wiley Eastern Ltd., New Delhi (1977).
I. A. Ibragimov and R. Z. Khas'minskii, Asymptotic Estimation Theory [in Russian], Nauka, Moscow (1979).
W. Eberl, “A note on characterization by sufficiency of the sample mean,” Publ. Math.,30, Nos. 1–2, 89–91 (1983).
A. M. Kagan, Yu. V. Linnik, and C. R. Rao, Characterization Problems of Mathematical Statistics [in Russian], Nauka, Moscow (1972).
Ch. Stein, “The admissibility of Pitman's estimator for a single location parameter,” Ann. Math. Stat.,30, No. 4, 970–979 (1959).
D. N. Shanbhag, “On some problems in distribution theory,” Sankhya, Ser. A,40, No. 2, 208–213 (1978).
V. P. Skitovich, “Linear forms of independent random variables and the normal distribution law,” Izv. Akad. Nauk SSSR, Ser. Math.,18, No. 2, 185–200 (1954).
G. Darmois, “Analyse generale de liaisons stochastiques,” Rev. Inst. Intern. Stat.,21, 2–8 (1953).
E. Lukacs, “A characterization of the gamma distribution,” Ann. Math. Stat.,26, No. 2, 319–324 (1955).
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Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei — Trudy Seminara, pp. 63–67, 1985.
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Kagan, A.M., Landsman, Z.M. An informational analog of the theorem of independence of sample mean and sample variance. J Math Sci 40, 499–502 (1988). https://doi.org/10.1007/BF01083644
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DOI: https://doi.org/10.1007/BF01083644