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Univariate Probability-G Classes for Scattered Samples under Different Forms of Hazard: Continuous and Discrete Version with Their Inferences Tests

Author

Listed:
  • Mohamed S. Eliwa

    (Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Muhammad H. Tahir

    (Department of Statistics, Faculty of Computing, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan)

  • Muhammad A. Hussain

    (Department of Statistics, Faculty of Computing, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan)

  • Bader Almohaimeed

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51482, Saudi Arabia)

  • Afrah Al-Bossly

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

  • Mahmoud El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

In this paper, we define a new generator to propose continuous as well as discrete families (or classes) of distributions. This generator is used for the DAL model (acronym of the last names of the authors, Dimitrakopoulou, Adamidis, and Loukas). This newly proposed family may be called the new odd DAL (NODAL) G-class or alternate odd DAL G-class of distributions. We developed both a continuous as well as discrete version of this new odd DAL G-class. Some mathematical and statistical properties of these new G-classes are listed. The estimation of the parameters is discussed. Some structural properties of two special models of these classes are described. The introduced generators can be effectively applied to discuss and analyze the different forms of failure rates including decreasing, increasing, bathtub, and J-shaped, among others. Moreover, the two generators can be used to discuss asymmetric and symmetric data under different forms of kurtosis. A Monte Carlo simulation study is reported to assess the performance of the maximum likelihood estimators of these new models. Some real-life data sets (air conditioning, flood discharges, kidney cysts) are analyzed to show that these newly proposed models perform better as compared to well-established competitive models.

Suggested Citation

  • Mohamed S. Eliwa & Muhammad H. Tahir & Muhammad A. Hussain & Bader Almohaimeed & Afrah Al-Bossly & Mahmoud El-Morshedy, 2023. "Univariate Probability-G Classes for Scattered Samples under Different Forms of Hazard: Continuous and Discrete Version with Their Inferences Tests," Mathematics, MDPI, vol. 11(13), pages 1-24, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2929-:d:1183209
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    References listed on IDEAS

    as
    1. Masood Anwar & Amna Bibi, 2018. "The Half-Logistic Generalized Weibull Distribution," Journal of Probability and Statistics, Hindawi, vol. 2018, pages 1-12, January.
    2. M. S. Eliwa & M. El-Morshedy, 2022. "A one-parameter discrete distribution for over-dispersed data: statistical and reliability properties with applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(10), pages 2467-2487, July.
    3. A. Asgharzadeh & Hassan S. Bakouch & M. Habibi, 2017. "A generalized binomial exponential 2 distribution: modeling and applications to hydrologic events," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2368-2387, October.
    4. Laleh Tafakori & Armin Pourkhanali & Saralees Nadarajah, 2018. "A new lifetime model with different types of failure rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(16), pages 4006-4020, August.
    5. 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.
    6. Amal S. Hassan & Said G. Nassr, 2019. "Power Lindley-G Family of Distributions," Annals of Data Science, Springer, vol. 6(2), pages 189-210, June.
    7. Kus, Coskun, 2007. "A new lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4497-4509, May.
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