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On the Omega Distribution: Some Properties and Estimation

Author

Listed:
  • Abdelaziz Alsubie

    (Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia)

  • Zuber Akhter

    (Department of Statistics, University of Delhi, Delhi 110 007, India)

  • Haseeb Athar

    (Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh 202 002, India)

  • Mahfooz Alam

    (Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh 202 002, India)

  • Abd EL-Baset A. Ahmad

    (Department of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt)

  • Gauss M. Cordeiro

    (Departamento de Estatística, Universidade Federal de Pernambuco, Recife 50710-165, Brazil)

  • Ahmed Z. Afify

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt)

Abstract

We obtain explicit expressions for single and product moments of the order statistics of an omega distribution. We also discuss seven methods to estimate the omega parameters. Various simulation results are performed to compare the performance of the proposed estimators. Furthermore, the maximum likelihood method is adopted to estimate the omega parameters under the type II censoring scheme. The usefulness of the omega distribution is proven using a real data set.

Suggested Citation

  • Abdelaziz Alsubie & Zuber Akhter & Haseeb Athar & Mahfooz Alam & Abd EL-Baset A. Ahmad & Gauss M. Cordeiro & Ahmed Z. Afify, 2021. "On the Omega Distribution: Some Properties and Estimation," Mathematics, MDPI, vol. 9(6), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:656-:d:520261
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    References listed on IDEAS

    as
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    2. Nadarajah, Saralees, 2008. "Explicit expressions for moments of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 196-205, February.
    3. Çağatay Çetinkaya & Ali İ. Genç, 2018. "Moments of order statistics of the standard two-sided power distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(17), pages 4311-4328, September.
    4. M. Nassar & A. Alzaatreh & M. Mead & O. Abo-Kasem, 2017. "Alpha power Weibull distribution: Properties and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10236-10252, October.
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