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Purely Sequential and k-Stage Procedures for Estimating the Mean of an Inverse Gaussian Distribution

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  • Ajit Chaturvedi

    (University of Delhi)

  • Sudeep R. Bapat

    (University of California)

  • Neeraj Joshi

    (University of Delhi)

Abstract

In the first part of this paper, we propose purely sequential and k-stage (k ≥ 3) procedures for estimation of the mean μ of an inverse Gaussian distribution having prescribed ‘proportional closeness’. The problem is constructed in such a manner that the boundedness of the expected loss is equivalent to the estimation of parameter with given ‘proportional closeness’. We obtain the associated second-order approximations for both the procedures. Second part of this paper deals with developing the minimum risk and bounded risk point estimation problems for estimating the mean μ of an inverse Gaussian distribution having unknown scale parameter λ. We propose an useful family of loss functions for both the problems and our aim is to control the associated risk functions. Moreover, we establish the failure of fixed sample size procedures to deal with these problems and hence propose purely sequential and k-stage (k ≥ 3) procedures to estimate the mean μ. We also obtain the second-order approximations associated with our sequential procedures. Further, we provide extensive sets of simulation studies and real data analysis to show the performances of our proposed procedures.

Suggested Citation

  • Ajit Chaturvedi & Sudeep R. Bapat & Neeraj Joshi, 2020. "Purely Sequential and k-Stage Procedures for Estimating the Mean of an Inverse Gaussian Distribution," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1193-1219, September.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09765-x
    DOI: 10.1007/s11009-019-09765-x
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    References listed on IDEAS

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    1. Sudeep R. Bapat, 2018. "On purely sequential estimation of an inverse Gaussian mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(8), pages 1005-1024, November.
    2. N. Mukhopadhyay & T. Solanky, 1997. "Estimation after sequential selection and ranking," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 95-106, January.
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    1. Ajit Chaturvedi & Sudeep R. Bapat & Neeraj Joshi, 2022. "Sequential Estimation of an Inverse Gaussian Mean with Known Coefficient of Variation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 402-420, May.

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