A Characterization of the Normal Law by the Property of Partial Sufficiency

1967 ◽  
Vol 12 (3) ◽  
pp. 512-514 ◽  
Author(s):  
A. M. Kagan ◽  
O. V. Shalaevskii
Keyword(s):  
Normal Law ◽  
Partial Sufficiency

A regressional characterization of the normal law

1987 ◽  
Vol 6 (1) ◽  
pp. 11-12
Author(s):  
Jacek Wesoł;owski
Keyword(s):  
Normal Law

scholarly journals On a conjecture of Seneta on regular variation of truncated moments

2021 ◽  
Vol 109 (123) ◽  
pp. 77-82
Author(s):  
Péter Kevei
Keyword(s):  
Distribution Function ◽  
Relative Stability ◽  
Regular Variation ◽  
Domain Of Attraction ◽  
Random Variable ◽  
Nonnegative Random Variable ◽  
Equivalent Characterization ◽  
Regularly Varying ◽  
Normal Law

We prove that h?(x) = ??x0 y??1F?(y)dy is regularly varying with index ? [0, ?) if and only if V?(x) = ?[0,x] y?dF(y) is regularly varying with the same index, where ? > 0, F(x) is a distribution function of a nonnegative random variable, and F?(x) = 1?F(x). This contains at ? = 0, ?= 1 a result of Rogozin [8] on relative stability, and at ? = 0, ? = 2 a new, equivalent characterization of the domain of attraction of the normal law. For ? = 0 and ? > 0 our result implies a recent conjecture by Seneta [9].

A characterization of the normal law

1969 ◽  
Vol 21 (1) ◽  
pp. 529-532
Author(s):  
R. P. Pakshirajan ◽  
N. R. Mohan
Keyword(s):  
Normal Law

scholarly journals Regularized distributions and entropic stability of Cramer’s characterization of the normal law

2016 ◽  
Vol 126 (12) ◽  
pp. 3865-3887 ◽  
Author(s):  
S.G. Bobkov ◽  
G.P. Chistyakov ◽  
F. Götze
Keyword(s):  
Normal Law

scholarly journals Characterization of normal law by a property of the non-central χ²-distribution

1967 ◽  
Vol 7 (1) ◽  
pp. 57-58
Author(s):  
A. Kagan ◽  
O. Shalaevsky
Keyword(s):  
Normal Law

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: А. М. Каган, О. В. Шалаевский. Характеризация нормального закона свойством нецентрального хи-квадрат распределения A. Kaganas, O. Šalajevskis. Normalinio dėsnio charakterizavimas necentrinio χ²-pasiskirstymo savybės pagalba

scholarly journals Chapter 15 Entropic instability of Cramer’s characterization of the normal law

2011 ◽  
pp. 231-242 ◽  
Author(s):  
S. G. Bobkov ◽  
G. P. Chistyakov ◽  
F. Götze
Keyword(s):  
Normal Law
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