Bounded Risk Estimation of the Gamma Scale Parameter in a Purely Sequential Sampling Procedure
Tóm tắt
We consider the purely sequential procedure for estimating the scale parameter of a gamma distribution with known shape parameter, when the risk function is bounded by the known preassigned number. In this paper, we provide asymptotic formulas for the expectation of the total sample size. Also, we propose how to adjust the stopping variable so that the risk is uniformly bounded by a known preassigned number. In the end, the performances of the proposed methodology are investigated with the help of simulations and also by using a real data set.
Tài liệu tham khảo
M. Woodroofe, Ann. Stat. 5 (1977), 984–995.
Y. Takada, Y. Nagata, J. Stat. Plan. Inference. 44 (1995), 277–289.
S. Zacks, A. Khan, Sequential Anal. 30 (2011), 297–307.
E. Isogai, C. Uno, Stat. Probab. Lett. 22 (1995), 287–293.
E. Mahmoudi, G. Roughani, Sequential Anal. 34 (2015), 25–38.
G. Roughani, E. Mahmoudi, Sequential Anal. 34 (2015), 387–405.
N. Starr, M. Woodroofe, Ann. Math. Stat. 43 (1972), 1147–1154.
N. Mukhopadhyay, Metrika. 27 (1980), 281–284.
E. Isogai, C. Uno, Ann. Inst. Stat. Math. 46 (1994), 77–82.
N. Mukhopadhyay, Ann. Inst. Stat. Math. 46 (1994), 509–519.
N. Mukhopadhyay, S. Datta, S. Afr. Stat. J. 29 (1995), 9–27. https://hdl.handle.net/10520/AJA0038271X_340
C. Uno, E. Isogai, D.L. Lim, Austrian J. Stat. 33 (2004), 281–291.
S. Zacks, N. Mukhopadhyay, Sequential Anal. 25 (2006), 437–452.
S. Zacks, N. Mukhopadhyay, Sequential Anal. 25 (2006), 203–226.
N. Mukhopadhyay, W. Pepe, Sequential Anal. 25 (2006), 85–101.
S. Zacks, Sequential Anal. 28 (2009), 69–81.
E. Mahmoudi, R. Lalehzari, Sequential Anal. 36 (2017), 38–54.
R. Lalehzari, E. Mahmoudi, A. Khalifeh, Sequential Anal. 37 (2018), 293–310.
C. Amero, M.J. Bayarri, J. Stat. Plan. Inference. 58 (1997), 241–261.
J. Choe, N. Shroff, in Proceeding of Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies, Washington, 1997, pp. 549–554.
R. Killick, I. Eckley, J. Stat. Softw. 58 (2014), 1–19.
J. Dopke, Int. J. Qual. Reliab. Manag. 11 (1994), 27–43.
D. Coit, T. Jin, IIE Trans. 32 (2000), 1161–1166.
A. Mareuil, R. Leconte, F. Brissette, M. Minville, Can. J. Civ. Eng. 34 (2007), 1048–1060.
Y. Takada, Sequential Anal. 5 (1986), 93–101.