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A New Class of the Power Function Distribution: Theory and Inference with an Application to Engineering Data

Author

Listed:
  • Alya Al Mutairi
  • Muhammad Z. Iqbal
  • Muhammad Z. Arshad
  • Ahmed Z. Afify

Abstract

In this study, a new class that generates optimal univariate models called a new exponentiated‐G class of distributions is developed. Numerous complementary statistical properties are derived and discussed in detail for the newly exponentiated power function (EPF) distribution. All possible shapes of the probability density and hazard rate functions are sketched for selected values of parameters. Six accredited estimation methods are discussed, and their performance is assessed and compared by a simulation study. The applicability of the new class is evaluated by analyzing the automotive engineering sector data.

Suggested Citation

  • Alya Al Mutairi & Muhammad Z. Iqbal & Muhammad Z. Arshad & Ahmed Z. Afify, 2022. "A New Class of the Power Function Distribution: Theory and Inference with an Application to Engineering Data," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1206254
    DOI: 10.1155/2022/1206254
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    References listed on IDEAS

    as
    1. Muhammad Z. Arshad & Muhammad Z. Iqbal & Alya Al Mutairi, 2021. "Statistical Properties of a New Bathtub Shaped Failure Rate Model With Applications in Survival and Failure Rate Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-49, June.
    2. 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.
    3. Muhammad Aslam & Christophe Ley & Zawar Hussain & Said Farooq Shah & Zahid Asghar, 2020. "A new generator for proposing flexible lifetime distributions and its properties," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-13, April.
    4. Zubair Ahmad & Eisa Mahmoudi & Morad Alizadeh & Rasool Roozegar & Ahmed Z. Afify & Markos Koutras, 2021. "The Exponential T-X Family of Distributions: Properties and an Application to Insurance Data," Journal of Mathematics, Hindawi, vol. 2021, pages 1-18, May.
    5. Alya Al Mutairi & Muhammad Z. Iqbal & Muhammad Z. Arshad & Badr Alnssyan & Hazem Al-Mofleh & Ahmed Z. Afify, 2021. "A New Extended Model with Bathtub-Shaped Failure Rate: Properties, Inference, Simulation, and Applications," Mathematics, MDPI, vol. 9(17), pages 1-32, August.
    6. 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.
    7. Alya Al Mutairi & Muhammad Z. Arshad, 2022. "A New Odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution With Theory and Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(2), pages 1-29, March.
    8. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.
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