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Moments and inferences of inverted topp-leone distribution based on record values

Author

Listed:
  • M. J. S. Khan

    (Aligarh Muslim University)

  • Farhan Ansari

    (Aligarh Muslim University)

  • Qazi J. Azhad

    (Shiv Nadar University Institute of Eminence)

  • Naresh Chandra Kabdwal

    (Banasthali Vidyapith)

Abstract

In this article, the explicit expression for the moments of record values is derived from the inverted Topp-Leone distribution. We have also derived the recurrence relation for single and product moments of the inverted Topp-Leone distribution based on record values. These results were utilized to obtain the best linear unbiased estimator for the location and scale parameter of the inverted Topp-Leone distribution. The best linear unbiased predictor of future record is also computed. Further, based on records, the maximum likelihood estimator for the scale and shape parameters of the inverted Topp-Leone distribution is also derived. Also, the exact confidence intervals for scale and shape parameters of the inverted Topp-Leone distribution are constructed in terms of upper records. We have also conducted a simulation study to show the performances of derived point and interval estimators. In addition to that, we have also presented a real data study to discuss the significance of derived results in real-life scenarios. This study is useful when the data are heavily right-tailed, follow an inverted Topp-Leone distribution, and are in the form of a record sequence.

Suggested Citation

  • M. J. S. Khan & Farhan Ansari & Qazi J. Azhad & Naresh Chandra Kabdwal, 2024. "Moments and inferences of inverted topp-leone distribution based on record values," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2623-2633, June.
    • Handle: RePEc:spr:ijsaem:v:15:y:2024:i:6:d:10.1007_s13198-024-02284-0
    DOI: 10.1007/s13198-024-02284-0
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    References listed on IDEAS

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    1. M. J. S. Khan & S. Iqrar, 2019. "On moments of dual generalized order statistics from Topp-Leone distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(3), pages 479-492, February.
    2. M. Basirat & S. Baratpour & Jafar Ahmadi, 2016. "On estimation of stress–strength parameter using record values from proportional hazard rate models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5787-5801, October.
    3. Ehab M. Almetwally, 2022. "The Odd Weibull Inverse Topp–Leone Distribution with Applications to COVID-19 Data," Annals of Data Science, Springer, vol. 9(1), pages 121-140, February.
    4. Zeeshan Ali & Azeem Ali & Gamze Ozel, 2021. "A modification in generalized classes of distributions: A new Topp–Leone class as an example," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(19), pages 4548-4570, August.
    5. Grigoriy Volovskiy & Udo Kamps, 2023. "Comparison of likelihood-based predictors of future Pareto and Lomax record values in terms of Pitman closeness," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(6), pages 1905-1922, March.
    6. M. A. Abd Elgawad & H. M. Barakat & S. Xiong, 2020. "Limit distributions of random record model in a stationary Gaussian sequence," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(5), pages 1099-1119, March.
    7. P. Yageen Thomas & Jerin Paul, 2019. "On diagnostic devices for proposing half-logistic and inverse half-logistic models using generalized (k) record values," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(5), pages 1073-1091, March.
    8. Sadegh Rezaei & Behnam Bahrami Sadr & Morad Alizadeh & Saralees Nadarajah, 2017. "Topp–Leone generated family of distributions: Properties and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(6), pages 2893-2909, March.
    9. Ali İ. Genç, 2017. "An absolutely continuous bivariate Topp–Leone distribution: A useful model on a bounded domain," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(19), pages 9726-9742, October.
    10. Jung In Seo & Yongku Kim, 2017. "Bayesian inference on extreme value distribution using upper record values," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(15), pages 7751-7768, August.
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