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Estimation with Modified Power Function Distribution Based on Order Statistics with Application to Evaporation Data

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Listed:
  • Devendra Kumar

    (Central University of Haryana)

  • Maneesh Kumar

    (Central University of Haryana)

  • J. P. Singh Joorel

    (University of Jammu)

Abstract

The modified power function distribution is an important distribution for analyzing the lifetime data, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub shaped failure rate. In this paper, we derive the exact explicit expressions for the single and double (product) of order statistics from the modified power function distribution. By using these relations, we have tabulated the expected values, second moments, variances and covariances of order statistics from samples of sizes up to 10 for various values of the parameters. Also, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on Type-II right-censored samples. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to one real data set.

Suggested Citation

  • Devendra Kumar & Maneesh Kumar & J. P. Singh Joorel, 2022. "Estimation with Modified Power Function Distribution Based on Order Statistics with Application to Evaporation Data," Annals of Data Science, Springer, vol. 9(4), pages 723-748, August.
    • Handle: RePEc:spr:aodasc:v:9:y:2022:i:4:d:10.1007_s40745-020-00244-6
    DOI: 10.1007/s40745-020-00244-6
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    References listed on IDEAS

    as
    1. Devendra Kumar & Sanku Dey & Saralees Nadarajah, 2017. "Extended exponential distribution based on order statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 9166-9184, September.
    2. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
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