IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i15p2328-d1442823.html
   My bibliography  Save this article

A New Generalization of the Uniform Distribution: Properties and Applications to Lifetime Data

Author

Listed:
  • Isidro Jesús González-Hernández

    (Department of Industrial Engineering, Universidad Autónoma del Estado de Hidalgo, Ciudad Sahagún 43998, Hidalgo, Mexico)

  • Luis Carlos Méndez-González

    (Department of Industrial Engineering and Manufacturing, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez 32310, Chihuahua, Mexico)

  • Rafael Granillo-Macías

    (Department of Industrial Engineering, Universidad Autónoma del Estado de Hidalgo, Ciudad Sahagún 43998, Hidalgo, Mexico)

  • José Luis Rodríguez-Muñoz

    (Department of Industrial Engineering, Universidad Autónoma del Estado de Hidalgo, Ciudad Sahagún 43998, Hidalgo, Mexico)

  • José Sergio Pacheco-Cedeño

    (Department of Industrial Engineering, Universidad Autónoma del Estado de Hidalgo, Ciudad Sahagún 43998, Hidalgo, Mexico)

Abstract

In this paper, we generalize two new statistical distributions, to improve the ability to model failure rates with non-monotonic, monotonic, and mainly bathtub curve behaviors. We call these distributions Generalized Powered Uniform Distribution and MOE-Powered Uniform. The proposed distributions’ approach is based on incorporating a parameter k in the power of the values of the random variables, which is associated with the Probability Density Function and includes an operator called the Powered Mean. Various statistical and mathematical features focused on reliability analysis are presented and discussed, to make the models attractive to reliability engineering or medicine specialists. We employed the Maximum Likelihood Estimator method to estimate the model parameters and we analyzed its performance through a Monte Carlo simulation study. To demonstrate the flexibility of the proposed approach, a comparative analysis was carried out on four case studies with the proposed MOE-Powered Uniform distribution, which can model failure times as a bathtub curve. The results showed that this new model is more flexible and useful for performing reliability analysis.

Suggested Citation

  • Isidro Jesús González-Hernández & Luis Carlos Méndez-González & Rafael Granillo-Macías & José Luis Rodríguez-Muñoz & José Sergio Pacheco-Cedeño, 2024. "A New Generalization of the Uniform Distribution: Properties and Applications to Lifetime Data," Mathematics, MDPI, vol. 12(15), pages 1-26, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2328-:d:1442823
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/15/2328/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/15/2328/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.
    2. Nadarajah, Saralees & Rocha, Ricardo, 2016. "Newdistns: An R Package for New Families of Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i10).
    3. Mohammed K. Shakhatreh, 2018. "A new three-parameter extension of the log-logistic distribution with applications to survival data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(21), pages 5205-5226, November.
    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. Abdisalam Hassan Muse & Samuel M. Mwalili & Oscar Ngesa, 2021. "On the Log-Logistic Distribution and Its Generalizations: A Survey," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-93, June.
    2. Refah Alotaibi & Ehab M. Almetwally & Indranil Ghosh & Hoda Rezk, 2022. "Classical and Bayesian Inference on Finite Mixture of Exponentiated Kumaraswamy Gompertz and Exponentiated Kumaraswamy Fréchet Distributions under Progressive Type II Censoring with Applications," Mathematics, MDPI, vol. 10(9), pages 1-23, April.
    3. Refah Alotaibi & Lamya A. Baharith & Ehab M. Almetwally & Mervat Khalifa & Indranil Ghosh & Hoda Rezk, 2022. "Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data," Mathematics, MDPI, vol. 10(15), pages 1-26, August.
    4. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.
    5. Zawar Hussain & Muhammad Aslam & Zahid Asghar, 2019. "On Exponential Negative-Binomial-X Family of Distributions," Annals of Data Science, Springer, vol. 6(4), pages 651-672, 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:12:y:2024:i:15:p:2328-:d:1442823. 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.