On estimation of stability in the problem of reconstructing symmetric types of distributions (Q1273378)

A set of distributions is called a complete type of distributions \(F\) if it consists of all distributions of the form \(F((x-a)/b)\), \(-\infty< a<\infty\), \(b>0\), and is called an additive type if it consists of all distributions of the form \(F(x-a)\), \(-\infty< a<\infty\). The type (complete or additive) of distributions \(F\) is called a symmetric type if for some values of the parameters (or parameter) the distribution function \(F((x-a)/ \sigma)\) (or \(F(x-a))\) is symmetric. New estimates of the stability characterizations of distribution types are obtained both for additive and complete types under the additional assumption that all distributions belong to symmetric types.