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

Mahmoud M. Mansour, Mohamed Ibrahim, Khaoula Aidi, Nadeem Shafique Butt, Mir Masoom Ali, Haitham M. Yousof and Mohamed S. Hamed
Additional contact information
Mahmoud M. Mansour: Management Information System Department, Yanbu, Taibah University, Yanbu 46421, Saudi Arabia
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

Mathematics, 2020, vol. 8, issue 9, 1-20

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.

Keywords: Bagdonavi?ius-Nikulin; Farlie-Gumbel-Morgenstern; Clayton Copula; censored validation; log-logistic distribution; Barzilai-Borwein; Burr XII Distribution; Censored Maximum Likelihood (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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