IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i9p1496-d806576.html
   My bibliography  Save this article

Classical and Bayesian Inference on Finite Mixture of Exponentiated Kumaraswamy Gompertz and Exponentiated Kumaraswamy Fréchet Distributions under Progressive Type II Censoring with Applications

Author

Listed:
  • Refah Alotaibi

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Ehab M. Almetwally

    (Department of Mathematical Statistical, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
    Department of Statistical, Faculty of Business Administration, Delta University for Science and Technology, Talkha 35712, Egypt)

  • Indranil Ghosh

    (Department of Mathematics and Statistics, University of North Carolina, Wilmington, NC 27599, USA)

  • Hoda Rezk

    (Department of Statistics, Al-Azhar University, Cairo 11751, Egypt)

Abstract

A finite mixture of exponentiated Kumaraswamy Gompertz and exponentiated Kumaraswamy Fréchet is developed and discussed as a novel probability model. We study some useful structural properties of the proposed model. To estimate the model parameters under the classical method, we use the maximum likelihood estimation using a progressive type II censoring scheme. Under the Bayesian paradigm the estimation is carried out with gamma priors under a progressive type II censored samples with squared error loss function. To demonstrate the efficiency of the proposed model based on progressively type II censoring, a simulation study is carried out. Three actual data sets are used as an example, demonstrating that the suggested model in the new class fits better than the existing finite mixture models available in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1496-:d:806576
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/9/1496/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/9/1496/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    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. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
    4. Gauss Cordeiro & Saralees Nadarajah & Edwin Ortega, 2012. "The Kumaraswamy Gumbel distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 139-168, June.
    5. Raqab, Mohammad Z. & Asgharzadeh, A. & Valiollahi, R., 2010. "Prediction for Pareto distribution based on progressively Type-II censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1732-1743, July.
    6. Biswabrata Pradhan & Debasis Kundu, 2009. "On progressively censored generalized exponential distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 497-515, November.
    7. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    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. 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.
    2. Refah Alotaibi & Ehab M. Almetwally & Qiuchen Hai & Hoda Rezk, 2022. "Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    3. M. Hermanns & E. Cramer, 2018. "Inference with progressively censored k-out-of-n system lifetime data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 787-810, December.
    4. Ritwik Bhattacharya & Biswabrata Pradhan, 2017. "Computation of optimum Type-II progressively hybrid censoring schemes using variable neighborhood search algorithm," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 802-821, December.
    5. Cramer, Erhard & Schmiedt, Anja Bettina, 2011. "Progressively Type-II censored competing risks data from Lomax distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1285-1303, March.
    6. Mazen Nassar & Refah Alotaibi & Chunfang Zhang, 2022. "Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data," Mathematics, MDPI, vol. 10(13), pages 1-25, June.
    7. Essam A. Ahmed, 2017. "Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1576-1608, July.
    8. Sukhdev Singh & Yogesh Mani Tripathi, 2018. "Estimating the parameters of an inverse Weibull distribution under progressive type-I interval censoring," Statistical Papers, Springer, vol. 59(1), pages 21-56, March.
    9. Essam AL-Hussaini & Alaa Abdel-Hamid & Atef Hashem, 2015. "One-sample Bayesian prediction intervals based on progressively type-II censored data from the half-logistic distribution under progressive stress model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 771-783, October.
    10. 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.
    11. Mazen Nassar & Refah Alotaibi & Ahmed Elshahhat, 2023. "Reliability Estimation of XLindley Constant-Stress Partially Accelerated Life Tests using Progressively Censored Samples," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    12. Park, Sangun & Ng, Hon Keung Tony & Chan, Ping Shing, 2015. "On the Fisher information and design of a flexible progressive censored experiment," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 142-149.
    13. Ahmed Soliman & N. Abou-elheggag & A. Abd ellah & A. Modhesh, 2012. "Bayesian and non-Bayesian inferences of the Burr-XII distribution for progressive first-failure censored data," METRON, Springer;Sapienza Università di Roma, vol. 70(1), pages 1-25, April.
    14. Rui Hua & Wenhao Gui, 2022. "Revisit to progressively Type-II censored competing risks data from Lomax distributions," Journal of Risk and Reliability, , vol. 236(3), pages 377-394, June.
    15. Olayan Albalawi & Naresh Chandra Kabdwal & Qazi J. Azhad & Rashi Hora & Basim S. O. Alsaedi, 2022. "Estimation of the Generalized Logarithmic Transformation Exponential Distribution under Progressively Type-II Censored Data with Application to the COVID-19 Mortality Rates," Mathematics, MDPI, vol. 10(7), pages 1-19, March.
    16. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.
    17. Wu, Shuo-Jye & Huang, Syuan-Rong, 2017. "Planning two or more level constant-stress accelerated life tests with competing risks," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 1-8.
    18. Bander Al-Zahrani & Areej M. AL-Zaydi, 2022. "Moments of progressively type-II censored order statistics from the complementary exponential geometric distribution and associated inference," 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(3), pages 1052-1065, June.
    19. Amel Abd-El-Monem & Mohamed S. Eliwa & Mahmoud El-Morshedy & Afrah Al-Bossly & Rashad M. EL-Sagheer, 2023. "Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    20. E. M. Almetwally & H. M. Almongy & M. K. Rastogi & M. Ibrahim, 2020. "Maximum Product Spacing Estimation of Weibull Distribution Under Adaptive Type-II Progressive Censoring Schemes," Annals of Data Science, Springer, vol. 7(2), pages 257-279, June.

    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:9:p:1496-:d:806576. 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.