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Estimating the shape parameter of a Pareto distribution under restrictions

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  • Yogesh Tripathi

  • Somesh Kumar

  • Constantinos Petropoulos

Abstract

In this paper estimation of the shape parameter of a Pareto distribution is considered under the a priori assumption that it is bounded below by a known constant. The loss function is scale invariant squared error. A class of minimax estimators is presented when the scale parameter of the distribution is known. In consequence, it has been shown that the generalized Bayes estimator with respect to the uniform prior on the truncated parameter space dominates the minimum risk equivariant estimator. By making use of a sequence of proper priors, we also show that this estimator is admissible for estimating the lower bounded shape parameter. A class of truncated linear estimators is studied as well. Some complete class results and a class of minimax estimators for the case of an unknown scale parameter are obtained. The corresponding generalized Bayes estimator is shown to be minimax in this case as well. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Yogesh Tripathi & Somesh Kumar & Constantinos Petropoulos, 2016. "Estimating the shape parameter of a Pareto distribution under restrictions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 91-111, January.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:1:p:91-111
    DOI: 10.1007/s00184-015-0545-9
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    References listed on IDEAS

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    1. Badiollah Asrabadi, 1990. "Estimation in the pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 199-205, December.
    2. Tatsuya Kubokawa, 2004. "Minimaxity in Estimation of Restricted Parameters," CIRJE F-Series CIRJE-F-270, CIRJE, Faculty of Economics, University of Tokyo.
    3. Rytgaard, Mette, 1990. "Estimation in the Pareto Distribution," ASTIN Bulletin, Cambridge University Press, vol. 20(2), pages 201-216, November.
    4. S. Saksena & A. Johnson, 1984. "Best unbiased estimators for the parameters of a two-parameter Pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 31(1), pages 77-83, December.
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    Cited by:

    1. Wenshu Qian & Wangxue Chen & Xiaofang He, 2021. "Parameter estimation for the Pareto distribution based on ranked set sampling," Statistical Papers, Springer, vol. 62(1), pages 395-417, February.

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