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A New Extended Cosine—G Distributions for Lifetime Studies

Author

Listed:
  • Mustapha Muhammad

    (School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
    Department of Mathematical Sciences, Bayero University Kano, Kano 700241, Nigeria)

  • Rashad A. R. Bantan

    (Department of Marine Geology, Faculty of Marines Science, King AbdulAziz University, Jeddah 21551, Saudi Arabia)

  • Lixia Liu

    (School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China)

  • Christophe Chesneau

    (Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France)

  • Muhammad H. Tahir

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

  • Farrukh Jamal

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

  • Mohammed Elgarhy

    (The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algarbia 31951, Egypt)

Abstract

In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.

Suggested Citation

  • Mustapha Muhammad & Rashad A. R. Bantan & Lixia Liu & Christophe Chesneau & Muhammad H. Tahir & Farrukh Jamal & Mohammed Elgarhy, 2021. "A New Extended Cosine—G Distributions for Lifetime Studies," Mathematics, MDPI, vol. 9(21), pages 1-29, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2758-:d:668610
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    References listed on IDEAS

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    1. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    2. Farrukh Jamal & Christophe Chesneau & Dalal Lala Bouali & Mahmood Ul Hassan, 2021. "Beyond the Sin-G family: The transformed Sin-G family," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-22, May.
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    5. Mahmoud, M.A.W. & Alam, Farouq Mohammad A., 2010. "The generalized linear exponential distribution," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1005-1014, June.
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    7. Bagheri, S.F. & Bahrami Samani, E. & Ganjali, M., 2016. "The generalized modified Weibull power series distribution: Theory and applications," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 136-160.
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    Cited by:

    1. Mustapha Muhammad & Lixia Liu & Badamasi Abba & Isyaku Muhammad & Mouna Bouchane & Hexin Zhang & Sani Musa, 2023. "A New Extension of the Topp–Leone-Family of Models with Applications to Real Data," Annals of Data Science, Springer, vol. 10(1), pages 225-250, February.
    2. Naif Alotaibi & A. S. Al-Moisheer & Ibrahim Elbatal & Mansour Shrahili & Mohammed Elgarhy & Ehab M. Almetwally, 2023. "Half Logistic Inverted Nadarajah–Haghighi Distribution under Ranked Set Sampling with Applications," Mathematics, MDPI, vol. 11(7), pages 1-32, April.
    3. Ahmad Abubakar Suleiman & Hanita Daud & Narinderjit Singh Sawaran Singh & Mahmod Othman & Aliyu Ismail Ishaq & Rajalingam Sokkalingam, 2023. "A Novel Odd Beta Prime-Logistic Distribution: Desirable Mathematical Properties and Applications to Engineering and Environmental Data," Sustainability, MDPI, vol. 15(13), pages 1-25, June.
    4. Salem A. Alyami & Ibrahim Elbatal & Naif Alotaibi & Ehab M. Almetwally & Mohammed Elgarhy, 2022. "Modeling to Factor Productivity of the United Kingdom Food Chain: Using a New Lifetime-Generated Family of Distributions," Sustainability, MDPI, vol. 14(14), pages 1-28, July.

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