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Estimation of the order restricted scale parameters for two populations from the Lomax distribution

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  • Constantinos Petropoulos

    (University of Patras)

Abstract

The usual methods of estimating the unknown parameters of a distribution, use only the information given from the sample data. In many cases, there is, also, another important information for estimating the unknown parameters of our model, such as the order of these parameters, and this last information improves the quality of estimation. In this paper, we deal with the problem of estimating the ordered scale parameters from two populations of the multivariate Lomax distribution, with unknown location parameters. It is proved that the best equivariant estimators of the scale parameters (in the unrestricted case) are not admissible and we construct estimators that improve upon the usual ones (when these parameters are known to be ordered).

Suggested Citation

  • Constantinos Petropoulos, 2017. "Estimation of the order restricted scale parameters for two populations from the Lomax distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 483-502, May.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:4:d:10.1007_s00184-017-0615-2
    DOI: 10.1007/s00184-017-0615-2
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    References listed on IDEAS

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    1. G. Vijayasree & Neeraj Misra & Harshinder Singh, 1995. "Componentwise estimation of ordered parameters ofk (≥2) exponential populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 287-307, June.
    2. Pal N. & Kushary D., 1992. "On Order Restricted Location Parameters Of Two Exponential Distributions," Statistics & Risk Modeling, De Gruyter, vol. 10(1-2), pages 133-152, February.
    3. Iliopoulos, George & Kourouklis, Stavros, 1999. "Improving on the Best Affine Equivariant Estimator of the Ratio of Generalized Variances," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 176-192, February.
    4. Amarjot Kaur & Harshinder Singh, 1991. "On the estimation of ordered means of two exponential populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 347-356, June.
    5. Kushary D. & Cohen A., 1989. "Estimating Ordered Location And Scale Parameters," Statistics & Risk Modeling, De Gruyter, vol. 7(3), pages 201-214, March.
    6. Carl M. Harris, 1968. "The Pareto Distribution as a Queue Service Discipline," Operations Research, INFORMS, vol. 16(2), pages 307-313, April.
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    Cited by:

    1. Lakshmi Kanta Patra & Suchandan Kayal & Somesh Kumar, 2021. "Minimax estimation of the common variance and precision of two normal populations with ordered restricted means," Statistical Papers, Springer, vol. 62(1), pages 209-233, February.
    2. Lakshmi Kanta Patra & Suchandan Kayal & Somesh Kumar, 2020. "Estimating a function of scale parameter of an exponential population with unknown location under general loss function," Statistical Papers, Springer, vol. 61(6), pages 2511-2527, December.

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