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

Author

Listed:
  • Zuber Akhter

    (University of Delhi)

  • Jagdish Saran

    (University of Delhi)

  • Kanika Verma

    (University of Delhi)

  • Narinder Pushkarna

    (University of Delhi)

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.

Suggested Citation

  • Zuber Akhter & Jagdish Saran & Kanika Verma & Narinder Pushkarna, 2022. "Moments of Order Statistics from Length-Biased Exponential Distribution and Associated Inference," Annals of Data Science, Springer, vol. 9(6), pages 1257-1282, December.
  • Handle: RePEc:spr:aodasc:v:9:y:2022:i:6:d:10.1007_s40745-020-00245-5
    DOI: 10.1007/s40745-020-00245-5
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    References listed on IDEAS

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    1. Mahmoud, M. A. W. & Sultan, K. S. & Amer, S. M., 2003. "Order statistics from inverse weibull distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 149-163, February.
    2. A. H. Khan & Mohd Yaqub & Saud Parvez, 1983. "Recurrence relations between moments of order statistics," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(3), pages 419-441, September.
    3. Mohamed Abdel Wahab Mahmoud & Khalaf Salman Sultan & Safaa Mousa Amer, 2003. "Order statistics from inverse Weibull distribution and characterizations," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 389-401.
    4. Nadarajah, Saralees, 2008. "Explicit expressions for moments of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 196-205, February.
    5. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    6. Ali Genç, 2012. "Moments of order statistics of Topp–Leone distribution," Statistical Papers, Springer, vol. 53(1), pages 117-131, February.
    7. Louzada, Francisco & Roman, Mari & Cancho, Vicente G., 2011. "The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2516-2524, August.
    8. P. Thomas & Philip Samuel, 2008. "Recurrence relations for the moments of order statistics from a beta distribution," Statistical Papers, Springer, vol. 49(1), pages 139-146, March.
    9. Broderick O. Oluyede & E. Olusegun George, 2002. "On stochastic inequalities and comparisons of reliability measures for weighted distributions," Mathematical Problems in Engineering, Hindawi, vol. 8, pages 1-13, January.
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