Sequential d-guaranteed estimate of the normal mean with bounded relative error

R.F. Salimov, I.N. Volodin, N.F. Nasibullina

Kazan Federal University, Kazan, 420008 Russia

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DOI: 10.26907/2541-7746.2019.1.145-151

For citation: Salimov R.F., Volodin I.N., Nasibullina N.F. Sequential d-guaranteed estimate of the normal mean with bounded relative error. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, vol. 161, no. 1, pp. 145–151. doi: 10.26907/2541-7746.2019.1.145-151.

Для цитирования: Salimov R.F., Volodin I.N., Nasibullina N.F. Sequential d-guaranteed estimate of the normal mean with bounded relative error // Учен. зап. Казан. ун-та. Сер. Физ.-матем. науки. – 2019. – Т. 161, кн. 1. – С. 145–151. – doi: 10.26907/2541- 7746.2019.1.145-151.

Abstract

In this paper, we continue our research on evaluation of the mean value of the normal distribution with prior information that this parameter is positive and very small. These data are obtained by using a prior exponential distribution with a large intensity parameter. The estimation problem with guaranteed relative error is considered. This issue is more important when small fractions are estimated. In addition to restrictions on the relative error, the procedure must have a given level of d-risk. We suggest a sequential procedure based on the first achievement by posterior probability of estimate reliability of a given level 1–β. The procedure is adapted to the problem of estimating harmful impurities in food products.

Keywords: first crossing procedure, normal mean estimation, d-posterior approach, sequential estimation

Acknowledgements. This work was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (project no. 1.7629.2017/8.9)

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Received

December 6, 2017

Salimov Rustem Faridovich, Assistant Lecturer of Department of Mathematical Statistics

Kazan Federal University

ul. Kremlevskaya, 18, Kazan, 420008 Russia

E-mail:  rustem.salimov@gmail.com

Volodin Igor Nikolaevich, Doctor of Physics and Mathematics, Professor of Department of Mathematical Statistics

Kazan Federal University

ul. Kremlevskaya, 18, Kazan, 420008 Russia

E-mail:  igorvolodin@gmail.com

Nasibullina Nailya Fergatevna, Student of Institute of Computational Mathematics and Information Technologies

Kazan Federal University

ul. Kremlevskaya, 18, Kazan, 420008 Russia

E-mail:  nasibusha@bk.ru

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