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In this paper, an application using the modified stochastic approxi-mation procedure which studied to answer the question for Robbins-Monroe procedure. The modified procedure depends on a new form. We use the case of loss system obey Negative Binomial distribution. The efficiency of the proposed procedure is calculated to determine the ways to improve the mentioned loss system, the results which are obtained show that our procedure can serve as a model of stochastic approximation with delayed observations. This new topic can be applied in many fields such as the biological, medical, life time experiments, and some industrial projects, to increase the production, where in our system we depend on, observe a lot items and this items are realized after random time delays. In this paper we referred to the conditions which improve the proposed loss system.
Harold J, Kushner J. Stochastic approximation with discontinuous dynamics and state dependent noise: W.P.1 and weak convergence. Journal of Mathematical Analysis and Applications 1981;82: 527-547.
Joseph, VR, Tian, Y. and Wu, CFJ. (2007). Adaptive Designs for Stochastic Root Finding. Statistica snica, 17, 1549-1565.
Konev V, Pergamenshchikov S. Sequential estimation in stochastic approximation with auto-regression errors in observations. Sequential Analysis. 2003;22:1-29.
Mahmoud MA, Rasha AA. Stochastic approximation with compound delayed observations. Math. Comput. Appl. 2005;10:283-289.
Zhu Y, Yin G. Stochastic approximation in real time: A pipe line approach. J. Compute Math. 1994;21:21-30.
Cheung Y, Elkind MSV. Stochastic approximation with virtual observations for dose-finding on discrete levels. Biometrika. 2010;97:109-121.
Rainer S, Harro W. On a stochastic approximation procedure based on averaging. Metrica. 1996;44: 165-180.
Bather JA. Stochastic approximation: A generalization of the robbins-monro procedure. In: Mandl P, Huškova M(eds) proc fourth Prague Symp Asymtotic Statistics Charles Univ. Prague. 1989;13- 27.
Paul H, Jones MC. A stochastic approximation method and its application to confidence interval. Journal of Computational and Graphical Statistics. 2009;18:184-200.
Dupač V, Herkenrath U. Stochastic approximation with delayed observations. Biometrika 72. 1985; 683-685.
Mahmoud MA, Rasha AA. Stochastic approximation and compound delayed observations with independent random time delay distribution. Arab J. Sci. Eng. 2011;36:1549-1558.
Mahmoud MA, Rasha AA, Waseem SW. Stochastic approximation with delayed components of observations and exact decreasing random time delay distribution. Sylwan Journal. 2015;159(5).
Mahmoud MA, Rasha AA, Waseem SW. Stochastic approximation with delayed groups of delayed multiservice observations and its applications. Bothalia Journal. 2016;46.
Nevelson MB, Khas Minski RZ. Stochastic approximation and recursive estimation. Nauka, Moscow. English trans. Amer. Soc.; 1976.
Harold J, Kushner J, Yin G. Stochastic approximation and recursive algorithm and applications. Appl. Math. 1997;35.