IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1035-d778302.html
   My bibliography  Save this article

A Modified Power Family of Distributions: Properties, Simulations and Applications

Author

Listed:
  • Mohamed Hussein

    (Department of Mathematics and Computer Science, Alexandria University, Alexandria 21544, Egypt
    Department of Business Administration, College of Business, King Khalid University, Abha 61421, Saudi Arabia)

  • Gauss M. Cordeiro

    (Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, Recife 520740, Brazil)

Abstract

In this paper, we present a new class of distributions called the modified power family by adding an extra shape parameter. Some of its structural properties are derived. Three special cases of the new family are considered and estimated using the method of maximum likelihood. The validity of the method of maximum likelihood is illustrated via Monte Carlo simulations. The importance and flexibility of the new family are empirically illustrated, partly due to efficient modeling of several real data. We compare the proposed family with some distributions and special models generated from other classes using classical statistical measures.

Suggested Citation

  • Mohamed Hussein & Gauss M. Cordeiro, 2022. "A Modified Power Family of Distributions: Properties, Simulations and Applications," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1035-:d:778302
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1035/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/7/1035/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Abbas Mahdavi & Debasis Kundu, 2017. "A new method for generating distributions with an application to exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6543-6557, July.
    2. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    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.
    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 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.
    2. 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.
    3. Abdulhakim A. Al-Babtain & Mohammed K. Shakhatreh & Mazen Nassar & Ahmed Z. Afify, 2020. "A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications," Mathematics, MDPI, vol. 8(8), pages 1-24, August.
    4. Ahmed Z. Afify & Osama Abdo Mohamed, 2020. "A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    5. Mashail M. AL Sobhi, 2020. "The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    6. 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.
    7. Mahmoud Aldeni & Carl Lee & Felix Famoye, 2017. "Families of distributions arising from the quantile of generalized lambda distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-18, December.
    8. 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.
    9. 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.
    10. 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.
    11. Gauss M. Cordeiro & Giovana O. Silva & Edwin M. M. Ortega, 2016. "An extended-G geometric family," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    12. Yaoting Yang & Weizhong Tian & Tingting Tong, 2021. "Generalized Mixtures of Exponential Distribution and Associated Inference," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    13. 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.
    14. Nicollas S. S. da Costa & Maria do Carmo Soares de Lima & Gauss Moutinho Cordeiro, 2024. "A Bimodal Exponential Regression Model for Analyzing Dengue Fever Case Rates in the Federal District of Brazil," Mathematics, MDPI, vol. 12(21), pages 1-20, October.
    15. 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.
    16. 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.
    17. Zubair Ahmad, 2020. "The Zubair-G Family of Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 7(2), pages 195-208, June.
    18. 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.
    19. Elizabeth Hashimoto & Gauss Cordeiro & Edwin Ortega, 2013. "The new Neyman type A beta Weibull model with long-term survivors," Computational Statistics, Springer, vol. 28(3), pages 933-954, June.
    20. 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.

    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:10:y:2022:i:7:p:1035-:d:778302. 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.