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This paper deals with the study of the performance of the shrinkage testimators under the invariant version of LINEX loss function for the scale parameter of an exponential distribution when type-II censored data are available.

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In the present article, some shrinkage testimators for the scale parameter of a two-parameter Weibull life testing model have been suggested under the LINEX loss function assuming the shape parameter is to be known. The comparisons of the proposed testimators have been made with the improved estimator.