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On the improved estimation of a function of the scale parameter of an exponential distribution based on doubly censored sample

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  • Lakshmi Kanta Patra

Abstract

In the present article, we have studied the estimation of entropy, that is, a function of scale parameter $\ln \sigma $ln⁡σ of an exponential distribution based on doubly censored sample when the location parameter is restricted to positive real line. The estimation problem is studied under a general class of bowl-shaped non monotone location invariant loss functions. It is established that the best affine equivariant estimator (BAEE) is inadmissible by deriving an improved estimator. This estimator is non-smooth. Further, we have obtained a smooth improved estimator. A class of estimators is considered and sufficient conditions are derived under which these estimators improve upon the BAEE. In particular, using these results we have obtained the improved estimators for the squared error and the linex loss functions. Finally, we have compared the risk performance of the proposed estimators numerically. One data analysis has been performed for illustrative purposes.

Suggested Citation

  • Lakshmi Kanta Patra, 2020. "On the improved estimation of a function of the scale parameter of an exponential distribution based on doubly censored sample," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(9), pages 1637-1651, June.
    • Handle: RePEc:taf:japsta:v:47:y:2020:i:9:p:1637-1651
    DOI: 10.1080/02664763.2019.1688261
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