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A New Probabilistic Approach: Estimation and Monte Carlo Simulation with Applications to Time-to-Event Data

Author

Listed:
  • Huda M. Alshanbari

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

  • Zubair Ahmad

    (Department of Statistics, Quaid-i-Azam University, Islamabad 44000, Pakistan)

  • Hazem Al-Mofleh

    (Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan)

  • Clement Boateng Ampadu

    (Independent Researcher, 31 Carrolton Road, Boston, MA 02132, USA)

  • Saima K. Khosa

    (Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK S7N 5E5, Canada)

Abstract

In this paper, we propose a useful method without adding any extra parameters to obtain new probability distributions. The proposed family is a combination of the two existing families of distributions and is called a weighted sine- G family. A two-parameter special member of the weighted sine- G family, using the Weibull distribution as a baseline model, is considered and investigated in detail. Some distributional properties of the weighted sine- G family are derived. Different estimation methods are considered to estimate the parameters of the special model of the weighted sine- G family. Furthermore, simulation studies based on these different methods are also provided. Finally, the applicability and usefulness of the weighted sine- G family are demonstrated by analyzing two data sets taken from the engineering sector.

Suggested Citation

  • Huda M. Alshanbari & Zubair Ahmad & Hazem Al-Mofleh & Clement Boateng Ampadu & Saima K. Khosa, 2023. "A New Probabilistic Approach: Estimation and Monte Carlo Simulation with Applications to Time-to-Event Data," Mathematics, MDPI, vol. 11(7), pages 1-30, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1583-:d:1106733
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    References listed on IDEAS

    as
    1. Zhuang, Liangliang & Xu, Ancha & Wang, Xiao-Lin, 2023. "A prognostic driven predictive maintenance framework based on Bayesian deep learning," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    2. Luo, Chunling & Shen, Lijuan & Xu, Ancha, 2022. "Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    3. 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.
    4. Hesham Reyad & Mustafa Ç. Korkmaz & Ahmed Z. Afify & G. G. Hamedani & Soha Othman, 2021. "The Fréchet Topp Leone-G Family of Distributions: Properties, Characterizations and Applications," Annals of Data Science, Springer, vol. 8(2), pages 345-366, June.
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    Cited by:

    1. Francisco Germán Badía & María D. Berrade, 2023. "Special Issue “Probability Theory and Stochastic Modeling with Applications”," Mathematics, MDPI, vol. 11(14), pages 1-3, July.

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