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Sequential Estimation of an Inverse Gaussian Mean with Known Coefficient of Variation

Author

Listed:
  • Ajit Chaturvedi

    (University of Delhi)

  • Sudeep R. Bapat

    (Indian Institute of Management)

  • Neeraj Joshi

    (University of Delhi)

Abstract

This paper deals with developing sequential procedures for estimating the mean of an inverse Gaussian (IG) distribution when the population coefficient of variation (CV) is known. We consider the minimum risk and bounded risk point estimation problems respectively. Moreover, we make use of a weighted squared-error loss function and aim to control the associated risk functions. Instead of the usual estimator, i.e., the sample mean, Searls J. Amer. Stat. Assoc. 50, 1225–1226 (1964) estimator is utilized for the purpose of estimation. Second-order approximations are also obtained under both estimation set-ups. We establish that Searls’ estimator dominates the usual estimator (sample mean) under proposed sequential sampling procedures. An extensive simulation analysis is carried out to validate the theoretical findings and real data illustrations are also provided to show the practical utility of our proposed sequential stopping strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:1:d:10.1007_s13571-021-00266-x
    DOI: 10.1007/s13571-021-00266-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. Katuomi Hirano & Kōsei Iwase, 1989. "Conditional information for an inverse Gaussian distribution with known coefficient of variation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 279-287, June.
    3. Antonio Punzo, 2019. "A new look at the inverse Gaussian distribution with applications to insurance and economic data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(7), pages 1260-1287, May.
    4. 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.
    5. Grzegorz Rempala & Richard Derrig, 2005. "Modeling Hidden Exposures in Claim Severity Via the Em Algorithm," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 108-128.
    Full references (including those not matched with items on IDEAS)

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