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Moments of Order Statistics from Length-Biased Exponential Distribution and Associated Inference

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Abstract

Dara and Ahmad (Recent advances in moment distribution and their hazard rates, Academic Publishing GmbH KG, Lap Lambert, 2012) proposed the length-biased exponential (LBE) distribution and proved that the LBE distribution is more flexible than the exponential distribution. In this paper, we have obtained new explicit algebraic expressions and some recurrence relations for both single and product moments of order statistics from LBE distribution. Further, these expressions are used to compute the means, variances and covariances of order statistics for different sample of sizes and for arbitrarily chosen parameter values. Next, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on complete as well as Type-II right censored samples. Finally, we carried out a simulation study to show the application of our results.

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Acknowledgements

The authors would like to express their gratitude to the referees and the editor for their constructive suggestions and comments.

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Authors and Affiliations

  1. Department of Statistics, University of Delhi, Delhi, 110 007, India

    Zuber Akhter, Jagdish Saran, Kanika Verma & Narinder Pushkarna

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  1. Zuber Akhter
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  2. Jagdish Saran
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Correspondence to Zuber Akhter.

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Akhter, Z., Saran, J., Verma, K. et al. Moments of Order Statistics from Length-Biased Exponential Distribution and Associated Inference. Ann. Data. Sci. 9, 1257–1282 (2022). https://doi.org/10.1007/s40745-020-00245-5

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  • DOI: https://doi.org/10.1007/s40745-020-00245-5

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