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Alternative approach to moments of order statistics from one-parameter Weibull distribution

Author

Listed:
  • Rai Piyush Kant

    (Dept. of Statistics, B.H.U. Varanasi, Varanasi, India .)

  • Sirohi Anu

    (Dept. of Mathematics and Statistics, Banasthali Vidyapith, Rajasthan, India .)

Abstract

The Weibull distribution is used to describe various observed failures of phenomena and widely used in survival analysis and reliability theory. Sometimes it is very difficult to compute moments of such distributions due to various reasons for e.g. analytical issues, multi parameter cases etc. This study presents the computation of the moments and the expected value of the product of order statistics in the sample from the one-parameter Weibull distribution. An alternative approach in connection to survival function is used to obtain these moments and expected values. In addition the characteristic function of the above distribution is also obtained in the form of gamma functions. Further an illustration is shown to find the first two moments and expected value of the product of order statistics by using this approach.

Suggested Citation

  • Rai Piyush Kant & Sirohi Anu, 2020. "Alternative approach to moments of order statistics from one-parameter Weibull distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 21(1), pages 155-162, March.
    • Handle: RePEc:vrs:stintr:v:21:y:2020:i:1:p:155-162:n:4
    DOI: 10.21307/stattrans-2020-010
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    References listed on IDEAS

    as
    1. Liang Hong, 2015. "Another Remark on the Alternative Expectation Formula," The American Statistician, Taylor & Francis Journals, vol. 69(3), pages 157-159, August.
    2. Liang Hong, 2012. "A Remark on the Alternative Expectation Formula," The American Statistician, Taylor & Francis Journals, vol. 66(4), pages 232-233, November.
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