A new method to estimate the stable degrees of some previous stability theorems based on the stability of the differential equations for characteristic functions (Q614268)

It is well known by the Geary theorem that a normal distribution is characterized by the independence of the sample mean and the sample variance. \textit{H. N. Hoang} [Theor. Probab. Appl. 13 (1968), 299--304 (1969); translation from Teor. Veroyatn. Primen. 13, 308--314 (1968; Zbl 0167.47404)] found an estimate of the stability of this characterization in the uniform metric. \textit{A. M. Kagan} [Sankhyā, Ser. A 32, 37--40 (1970; Zbl 0206.20103)] considered the stability of the characterization of a normal distribution based on the condition of admissibility of the sample mean as an estimator of a shift parameter. The authors give other estimates of stability of these characterization theorems in another metric.