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A New Log-Logistic Lifetime Model with Mathematical Properties, Copula, Modified Goodness-of-Fit Test for Validation and Real Data Modeling

Author

Listed:
  • Mahmoud M. Mansour

    (Management Information System Department, Yanbu, Taibah University, Yanbu 46421, Saudi Arabia
    Department of Statistics, Mathematics and Insurance, Benha University, Benha 13513, Egypt)

  • Mohamed Ibrahim

    (Department of Applied Statistics and Insurance, Faculty of Commerce, Damietta University, Damietta 34519, Egypt)

  • Khaoula Aidi

    (Laboratory of Probability and Statistics LaPS, University Badji Mokhtar, Annaba 23000, Algeria)

  • Nadeem Shafique Butt

    (Department of Family and Community Medicine, King Abdul Aziz University, Jeddah 21589, Saudi Arabia)

  • Mir Masoom Ali

    (Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA)

  • Haitham M. Yousof

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13513, Egypt)

  • Mohamed S. Hamed

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13513, Egypt)

Abstract

After defining a new log-logistic model and studying its properties, some new bivariate type versions using “Farlie-Gumbel-Morgenstern Copula”, “modified Farlie-Gumbel-Morgenstern Copula”, “Clayton Copula”, and “Renyi’s entropy Copula” are derived. Then, using the Bagdonavicius-Nikulin goodness-of-fit (BN-GOF) test for validation, we proposed a goodness-of-fit test for a new log-logistic model. The modified test is applied for the “right censored” real dataset of survival times. All elements of the modified test are explicitly derived and given. Three real data applications are presented for measuring the flexibility and the importance of the new model under the uncensored scheme. Two other real datasets are analyzed for censored validation.

Suggested Citation

  • Mahmoud M. Mansour & Mohamed Ibrahim & Khaoula Aidi & Nadeem Shafique Butt & Mir Masoom Ali & Haitham M. Yousof & Mohamed S. Hamed, 2020. "A New Log-Logistic Lifetime Model with Mathematical Properties, Copula, Modified Goodness-of-Fit Test for Validation and Real Data Modeling," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1508-:d:408952
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    References listed on IDEAS

    as
    1. Hafida Goual & Haitham M. Yousof, 2020. "Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(3), pages 393-423, February.
    2. Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2004. "A new class of bivariate copulas," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 315-325, February.
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    Cited by:

    1. Yousof Haitham M. & Masoom Ali M. & Goual Hafida & Ibrahim Mohamed, 2021. "A new reciprocal Rayleigh extension: properties, copulas, different methods of estimation and a modified right-censored test for validation," Statistics in Transition New Series, Statistics Poland, vol. 22(3), pages 99-121, September.
    2. Heba Soltan Mohamed & M. Masoom Ali & Haitham M. Yousof, 2023. "The Lindley Gompertz Model for Estimating the Survival Rates: Properties and Applications in Insurance," Annals of Data Science, Springer, vol. 10(5), pages 1199-1216, October.
    3. Mohamed Ibrahim & M. Masoom Ali & Haitham M. Yousof, 2023. "The Discrete Analogue of the Weibull G Family: Properties, Different Applications, Bayesian and Non-Bayesian Estimation Methods," Annals of Data Science, Springer, vol. 10(4), pages 1069-1106, August.
    4. Mohamed Ibrahim & Khaoula Aidi & M. Masoom Ali & Haitham M. Yousof, 2023. "A Novel Test Statistic for Right Censored Validity under a new Chen extension with Applications in Reliability and Medicine," Annals of Data Science, Springer, vol. 10(5), pages 1285-1299, October.

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