IDEAS home Printed from https://ideas.repec.org/a/wly/complx/v2022y2022i1n2219570.html

Marshall–Olkin Extended Gumbel Type‐II Distribution: Properties and Applications

Author

Listed:
  • Farwa Willayat
  • Naz Saud
  • Muhammad Ijaz
  • Anita Silvianita
  • Mahmoud El-Morshedy

Abstract

Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type‐II (MOEGT‐II) which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J‐shaped, and upside down bathtub shapes of the failure rate function. Various statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT‐II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT‐II distribution have been shown using three real life data sets. The MOEGT‐II distribution has been demonstrated as better fit than Exponentiated Gumbel Type‐II (EGT‐II), Marshall–Olkin Gumbel Type‐II (MOGT‐II), Gumbel Type‐II (GT‐II), Marshall–Olkin–Frechet (MOF), Frechet (F), Burr III, Log Logistic (LL), Beta Inverse Weibull (BIW), and Kumaraswamy Inverse Weibull (KIW) distributions.

Suggested Citation

  • Farwa Willayat & Naz Saud & Muhammad Ijaz & Anita Silvianita & Mahmoud El-Morshedy, 2022. "Marshall–Olkin Extended Gumbel Type‐II Distribution: Properties and Applications," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:2219570
    DOI: 10.1155/2022/2219570
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/2219570
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/2219570?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Al-Hasan, Mohammed & Nigmatullin, Raoul R., 2003. "Identification of the generalized Weibull distribution in wind speed data by the Eigen-coordinates method," Renewable Energy, Elsevier, vol. 28(1), pages 93-110.
    2. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Extended Gumbel Type-2 Distribution: Properties and Applications," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-11, November.
    3. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
    4. I. E. Okorie & A. C. Akpanta & J. Ohakwe, 2016. "The Exponentiated Gumbel Type-2 Distribution: Properties and Application," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-10, August.
    5. Ehab M. Almetwally & Mohamed A. H. Sabry & Randa Alharbi & Dalia Alnagar & Sh. A. M. Mubarak & E. H. Hafez & Ahmed Mostafa Khalil, 2021. "Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type-I and Type-II Censoring," Complexity, Hindawi, vol. 2021, pages 1-18, March.
    6. Muhammad Ahsan Ul Haq & G. G. Hamedani & M. Elgarhy & Pedro Luiz Ramos, 2020. "Marshall-Olkin Power Lomax Distribution: Properties and Estimation Based on Complete and Censored Samples," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(1), pages 1-48, January.
    7. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Extended Gumbel Type‐2 Distribution: Properties and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    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. Hadeel Klakattawi & Dawlah Alsulami & Mervat Abd Elaal & Sanku Dey & Lamya Baharith, 2022. "A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-29, February.
    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. Ibrahim E. Ragab & Najwan Alsadat & Mustapha Muhammad & Suleman Nasiru & Mohammed Elgarhy, 2025. "Modeling to Engineering and Failure Times Data: Using the Marshall–Olkin Extended Exponential Distribution," Advances in Mathematical Physics, John Wiley & Sons, vol. 2025(1).
    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. Saralees Nadarajah & Božidar Popović & Miroslav Ristić, 2013. "Compounding: an R package for computing continuous distributions obtained by compounding a continuous and a discrete distribution," Computational Statistics, Springer, vol. 28(3), pages 977-992, June.
    6. Zubair Ahmad, 2020. "The Zubair-G Family of Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 7(2), pages 195-208, June.
    7. Yolanda M. Gómez & Diego I. Gallardo & Carolina Marchant & Luis Sánchez & Marcelo Bourguignon, 2023. "An In-Depth Review of the Weibull Model with a Focus on Various Parameterizations," Mathematics, MDPI, vol. 12(1), pages 1-19, December.
    8. El Alimi, Souheil & Maatallah, Taher & Dahmouni, Anouar Wajdi & Ben Nasrallah, Sassi, 2012. "Modeling and investigation of the wind resource in the gulf of Tunis, Tunisia," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(8), pages 5466-5478.
    9. Jose K. K. & Sivadas Remya, 2015. "Negative Binomial Marshall–Olkin Rayleigh Distribution and Its Applications," Stochastics and Quality Control, De Gruyter, vol. 30(2), pages 89-98, December.
    10. Rocha, Ricardo & Nadarajah, Saralees & Tomazella, Vera & Louzada, Francisco, 2017. "A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 48-63.
    11. Rania A. H. Mohamed & Abdulhakim A. Al-Babtain & I. Elbatal & Ehab M. Almetwally & Hisham M. Almongy, 2022. "[Retracted] Classical and Bayesian Inference of Marshall‐Olkin Extended Gompertz Makeham Model with Modeling of Physics Data," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    12. Gugliani, G.K. & Sarkar, A. & Ley, C. & Mandal, S., 2018. "New methods to assess wind resources in terms of wind speed, load, power and direction," Renewable Energy, Elsevier, vol. 129(PA), pages 168-182.
    13. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    14. R Alshenawy & Hanan Haj Ahmad & Ali Al-Alwan, 2022. "Progressive censoring schemes for marshall-olkin pareto distribution with applications: Estimation and prediction," PLOS ONE, Public Library of Science, vol. 17(7), pages 1-20, July.
    15. Mehdi Basikhasteh & Iman Makhdoom, 2022. "Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions," 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. 13(2), pages 867-880, April.
    16. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Extended Gumbel Type‐2 Distribution: Properties and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    17. Muhammad Ijaz & Syed Muhammad Asim & Alamgir & Muhammad Farooq & Sajjad Ahmad Khan & Sadaf Manzoor, 2020. "A Gull Alpha Power Weibull distribution with applications to real and simulated data," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    18. Abukari Abdul-Lateef & Amadu Yakubu & Shei Baba Sayibu, 2024. "On the Topp-Leone Generalized Power Weibull Distribution: Properties, Applications and Regression," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 13(2), pages 1-1.
    19. Nanda, Asok K. & Das, Suchismita, 2012. "Stochastic orders of the Marshall–Olkin extended distribution," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 295-302.
    20. Ehsan Fayyazishishavan & Serpil Kılıç Depren, 2021. "Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-12, April.

    More about this item

    Statistics

    Access and download statistics

    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:wly:complx:v:2022:y:2022:i:1:n:2219570. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/8503 .

    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.