IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i6p656-d520261.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/6/656/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/6/656/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    3. Jemilohun Vincent Gbenga & Ipinyomi Reuben Adeyemi, 2022. "Alpha Power Extended Inverse Weibull Poisson Distribution: Properties, Inference, and Applications to lifetime data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(1), pages 1-10, March.
    4. Hadeel S Klakattawi, 2022. "Survival analysis of cancer patients using a new extended Weibull distribution," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-20, February.
    5. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-90, November.
    6. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    7. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    8. Showkat Ahmad Lone & Tabassum Naz Sindhu & Marwa K. H. Hassan & Tahani A. Abushal & Sadia Anwar & Anum Shafiq, 2023. "Theoretical Structure and Applications of a Newly Enhanced Gumbel Type II Model," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    9. Refah Alotaibi & Mazen Nassar & Hoda Rezk & Ahmed Elshahhat, 2022. "Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(16), pages 1-21, August.
    10. Abdulkareem M. Basheer, 2022. "Marshall–Olkin Alpha Power Inverse Exponential Distribution: Properties and Applications," Annals of Data Science, Springer, vol. 9(2), pages 301-313, April.
    11. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    12. MirMostafaee, S.M.T.K., 2014. "On the moments of order statistics coming from the Topp–Leone distribution," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 85-91.
    13. Joseph Thomas Eghwerido & Pelumi E. Oguntunde & Friday Ikechukwu Agu, 2023. "The Alpha Power Marshall-Olkin-G Distribution: Properties, and Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 172-197, February.
    14. T. Ogura & H. Murakami, 2014. "A rank test based on the moments of order statistics of the modified Makeham distribution," Computational Statistics, Springer, vol. 29(6), pages 1691-1711, December.
    15. Charlotte Truchet & Alejandro Arbelaez & Florian Richoux & Philippe Codognet, 2016. "Estimating parallel runtimes for randomized algorithms in constraint solving," Journal of Heuristics, Springer, vol. 22(4), pages 613-648, August.
    16. Ali Genç, 2012. "Moments of order statistics of Topp–Leone distribution," Statistical Papers, Springer, vol. 53(1), pages 117-131, February.
    17. Aly, Emad-Eldin A.A., 2020. "On order statistics from Laplace-type distributions," Statistics & Probability Letters, Elsevier, vol. 160(C).
    18. Pescim, Rodrigo R. & Demétrio, Clarice G.B. & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Urbano, Mariana R., 2010. "The beta generalized half-normal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 945-957, April.
    19. Emrah ALTUN & Morad ALIZADEH & Gamze OZEL & Hüseyin TATLIDIL & Najmieh MAKSAYI, 2017. "Forecasting Value-At-Risk With Two-Step Method: Garch-Exponentiated Odd Log-Logistic Normal Model," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 97-115, December.
    20. Zhe Chen & F. Douglas Foster & David R. Gallagher & Adrian D. Lee & Steven Cahan, 2015. "A model of emulation funds," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 55(3), pages 717-748, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:656-:d:520261. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.