Abstract
A class of nonparametric kernel estimates is suggested for an unknown hazard rate function and its derivative. Distribution and mean square convergences of the proposed estimates to the unknown hazard function and its derivative are proved. These estimates can be used for solving the problems of operational reliability of complex physical, technical, and program systems under uncertainty conditions.
Similar content being viewed by others
References
E. Yu. Barzilovich, Yu. K. Belyaev, V. A. Kashtanov, et al., Problems of the Mathematical Theory of Reliability, Radio I Svyaz' [in Russian], Moscow (1983), 376 pp.
A. A. Borovkov, Mathematical Statistics [in Russian], Nauka, Novosibirsk (1977), 772 pp.
A. V. Kitaeva and G. M. Koshkin, Avtomat. Telemekh., No. 3, 202–214 (1997).
A. V. Dobrovidov and G. M. Koshkin, Nonparametric Estimation of Signals [in Russian], Nauka, Moscow (1997), 336 pp.
V. A. Vaal' and G. M. Koshkin, in: Mathematical Modeling and Probability Theory. Collection of Scientific Papers [in Russian], Peleng Publishing House, Tomsk (1998), pp. 147–149.
G. M. Koshkin, Sib. Mat. Zh.,40, 1999 (in print).
H. Cramer, Methods of Mathematical Statistics [Russian translation], Mir, Moscow (1975), 648 pp.
Additional information
State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 141–146, March, 1999.
Rights and permissions
About this article
Cite this article
Vaal', V.A., Koshkin, G.M. Nonparametric estimation of the hazard rate function and its derivative. Russ Phys J 42, 362–366 (1999). https://doi.org/10.1007/BF02508324
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02508324