Guaranteeing confidence estimation of parameters for a set of distributions

Аuthors

Kan A. V.^*, Kan Y. S.^**

National Research Center "Zhukovsky Institut", 1, Zhukovsky str, Zhukovsky, Moscow Region, 140180, Russia

*e-mail: avkan@nrczh.ru
**e-mail: yu_kan@mail.ru

Abstract

A problem under consideration is parametric estimation based on some sample of finite size in the case where the Central Limit Theorem (CLT) is applied to construct asymptotic confidence intervals. It is suggested to construct guaranteeing confidence intervals taking into account an inaccuracy of the CLT normal approximation. Such intervals are constructed explicitly for some unknown parameter of the exponential distribution and also for some unknown probability.