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Abstract
In this paper, a modified Chi-square goodness-of-fit test called the modified BagdonaviÄius-Nikulin goodness-of-fit test statistic is investigated and the applied for distributional validation under the right censored case. The new modified goodness-of-fit test is presented and applied for the right censored data sets. The algorithm of the censored Barzilai-Borwein is employed via a comprehensive simulation study for assessing validity of the new test. The modified BagdonaviÄius-Nikulin test is applied to four real and right censored data sets. A new distribution is compared with many other competitive distributions under the new modified BagdonaviÄius-Nikulin goodness-of-fit test statistic.
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References
- Abouelmagd, T. H. M., Hamed, M. S., Handique, L., Goual, H., Ali, M. M., Yousof, H. M. and Korkmaz, M. C. (2019a). A new class of distributions based on the zero truncated Poisson distribution with properties and applications, 12(3), 152-164.
- Abouelmagda, T. H. M., Hameda, M. S., Hamedanib, G. G., Alic, M. M., Goual, H., Korkmaze, M. C. and Yousof, H. M. (2019b). The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and valida-tion test. Journal of Nonlinear Sciences and Applications, 12(5), 314-336.â€
- Aidi, K., Butt, N. S., Ali, M. M., Ibrahim, M., Yousof, H. M. and Shehata, W. A. M. (2021). A Modified Chi-square Type Test Statistic for the Double Burr X Model with Applications to Right Censored Medical and Reliability Data. Pakistan Journal of Statistics and Operation Research, 17(3), 615-623.
- Al-Babtain, A. A., Elbatal, I. and Yousof, H. M. (2020a). A new three parameter Fréchet model with mathematical properties and applications. Journal of Taibah University for Science, 14(1), 265-278.â€
- Al-babtain, A. A., Elbatal, I. and Yousof, H. M. (2020b). A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data. Symmetry, 12(3), 440.â€
- Alizadeh, M., Rasekhi, M., Yousof, H. M., Ramires, T. G. and Hamedani G. G. (2018). Extended exponentiated Nadarajah-Haghighi model: mathematical properties, characterizations and applications. Studia Scientiarum Mathematicarum Hungarica, 55, 498-522.
- BagdonaviÄius, V.; Nikulin, M. (2011a). Chi-squared Goodness-of-fit test for right censored Data. Int. J. Appl. Math. Stat., 24, 30-50.
- BagdonaviÄius, V.; Nikulin, M. (2011b). Chi-squared tests for general composite hypotheses from censored samples Comptes Rendus de lácadémie des Sciences de Paris. Mathématiques, 349, 219-223.
- Crowder, M. J., Kimber A. C., Smith R. L and Sweeting, T. J. (1991). Statistical analysis of reliability data, CHAPMAN &HALL/CRC
- Dias, C. R. B., Alizadeh, M. and Cordeiro, G. M. (2018). The beta Nadarajah-Haghighi distribution. Hacettepe Journal of Mathematics and Statistics, 47, 1302 1323.
- Elgohari, H. and Yousof, H. M. (2020a). A Generalization of Lomax Distribution with Properties, Copula and Real Data Applications. Pakistan Journal of Statistics and Operation Research, 16(4), 697-711.
- Elgohari, H. and Yousof, H. M. (2020b). New Extension of Weibull Distribution: Copula, Mathematical Properties and Data Modeling. Statistics, Optimization & Information Computing, 8(4), 972-993.
- Elsayed, H. A. H. and Yousof, H. M. (2019). The Burr X Nadarajah Haghighi distribution: statistical properties and application to the exceedances of flood peaks data. Journal of Mathematics and Statistics, 15, 146-157.
- Galanova, N.; Lemeshko, B.Y.; Chimitova, E.V. (2012). Using Nonparametric Goodness-of-Fit Tests to Validate Accelerated Failure Time Models. Optoelectron. Instrum. Data Process, 48, 580-592.
- Goual, H. and Yousof, H. M. (2020). Validation of Burr XII inverse Rayleigh model via a modified Chi-squared goodness-of-fit test. Journal of Applied Statistics, 47(3), 393-423.
- Goual, H., Yousof, H. M. and Ali, M. M. (2019). Validation of the odd Lindley exponentiated exponential by a modified goodness of fit test with applications to censored and complete data. Pakistan Journal of Statistics and Operation Research, 15(3), 745-771.
- Goual, H., Yousof, H. M. and Ali, M. M. (2020). Lomax inverse Weibull model: properties, applications, and a modified Chi-squared goodness-of-fit test for validation. Journal of Nonlinear Sciences & Applications (JNSA), 13(6), 330-353.
- Habib, M.G.; Thomas, D.R. (1986). Chi-squared goodness-of-fit tests for randomly censored Data. Ann. Stat, 14, 759-765.
- Hollander, M.; Pena, E. (1992). Chi-square goodness-of-fit test for randomly censored data. JASA, 87, 458-463.
- Ibrahim, M. (2020). The generalized odd Log-logistic Nadarajah Haghighi distribution: statistical properties and different methods of estimation. Journal of Applied Probability and Statistics, 15(2), 61-84.
- Ibrahim, M., Aidi, K., Ali, M. M. and Yousof, H. M. (2021). A Novel Test Statistic for Right Censored Validity under a new Chen extension with Applications in Reliability and Medicine. Annals of Data Science, forthcoming.
- Ibrahim, M., Altun, E., Goual, H., and Yousof, H. M. (2021). Modified goodness-of-fit type test for censored validation under a new Burr type XII distribution with different methods of estimation and regression modeling. Eurasian Bulletin of Mathematics, 3(3), 162-182.â€
- Ibrahim, M., Yadav, A. S., Yousof, H. M., Goual, H. and Hamedani, G. G. (2019). A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation. Communications for Statistical Applications and Methods, 26(5), 473-495.â€
- John, P. Klein, Melvin L. Moeschberger (1997). Survival Analysis: Techniques for Censored and Truncated Data, Statistics for Biology and Health.
- Lemonte, A. J. (2013). A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function. Computational Statistics and Data Analysis, 62, 149-170.
- Lemonte, A. J., Cordeiro, G. M. and Moreno--Arenas, G. (2016). A new useful three-parameter extension of the exponential distribution. Statistics, 50, 312-337.
- Mansour, M. M., Ibrahim, M., Aidi, K., Shafique Butt, N., Ali, M. M., Yousof, H. M. and Hamed, M. S. (2020a). A New Log-Logistic Lifetime Model with Mathematical Properties, Copula, Modified Goodness-of-Fit Test for Validation and Real Data Modeling. Mathematics, 8(9), 1508.â€
- Mansour, M. M., Butt, N. S., Ansari, S. I., Yousof, H. M., Ali, M. M. and Ibrahim, M. (2020b). A new exponentiated Weibull distribution's extension: copula, mathematical properties and applications. Contributions to Mathematics, 1 (2020) 57-66. DOI: 10.47443/cm.2020.0018
- Mansour, M., Korkmaz, M. Ç., Ali, M. M., Yousof, H. M., Ansari, S. I. and Ibrahim, M. (2020c). A generalization of the exponentiated Weibull model with properties, Copula and application. Eurasian Bulletin of Mathematics, 3(2), 84-102.â€
- Mansour, M., Rasekhi, M., Ibrahim, M., Aidi, K., Yousof, H. M. and Elrazik, E. A. (2020d). A New Parametric Life Distribution with Modified BagdonaviÄius-Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods. Entropy, 22(5), 592.â€
- Mansour, M., Yousof, H. M., Shehata, W. A. M. and Ibrahim, M. (2020e). A new two parameter Burr XII distribution: properties, copula, different estimation methods and modeling acute bone cancer data. Journal of Nonlinear Science and Applications, 13(5), 223-238.
- Mansour, M. M., Butt, N. S., Yousof, H. M., Ansari, S. I. and Ibrahim, M. (2020f). A Generalization of Reciprocal Exponential Model: Clayton Copula, Statistical Properties and Modeling Skewed and Symmetric Real Data Sets. Pakistan Journal of Statistics and Operation Research, 16(2), 373-386.â€
- Nadarajah, S.and Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45, 543--558.
- Ortiga, E. M., Lemonte, A. J., Silva, G. O. and Cordeiro, G. M. (2015). New flexible models generated by gamma random variables for lifetime modeling. Journal of Applied Statistics, 42(10), 2159-2179.
- Nascimento, A. D., Silva, K. F., Cordeiro, G. M., Alizadeh, M., Yousof, H. M. and Hamedani, G. G. (2019). The odd Nadarajah-Haghighi family of distributions: properties and applications. Studia Scientiarum Mathematicarum Hungarica, 56(2), 185-210.
- Ravi, V. and Gilbert, P. D. (2009). BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function, J. Statist. Software, 32(4).
- Salah, M. M., El-Morshedy, M., Eliwa, M. S. and Yousof, H. M. (2020). Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing. Mathematics, 8(11), 1949.â€
- Shehata, W. A. M. and Yousof, H. M. (2021). The four-parameter exponentiated Weibull model with Copula, properties and real data modeling. Pakistan Journal of Statistics and Operation Research, 17(3), 649-667.
- Yadav, A. S., Goual, H., Alotaibi, R. M., Ali, M. M. and Yousof, H. M. (2020). Validation of the Topp-Leone-Lomax model via a modified Nikulin-Rao-Robson goodness-of-fit test with different methods of estimation. Symmetry, 12(1), 57.â€
- Yousof, H. M., Afify, A. Z., Hamedani, G. G. and Aryal, G. (2017). The Burr X generator of distributions for lifetime data. Journal of Statistical Theory and Applications, 16, 288-305.
- Yousof, H. M., Aidi, K., Hamedani, G. G and Ibrahim, M. (2021a). A new parametric lifetime distribution with modified Chi-square type test for right censored validation, characterizations and different estimation methods. Pakistan Journal of Statistics and Operation Research, 17(2), 399-425.
- Yousof, H. M., Ali, M. M., Goual, H. and Ibrahim. M. (2021b). A new reciprocal Rayleigh extension: properties, copulas, different methods of estimation and modified right censored test for validation, Statistics in Transition New Series, 23(3), 1-23.
- Yousof, H. M., Ali, M. M., Hamedani, G. G., Aidi, K. and Ibrahim, M. (2021c). A new lifetime distribution with properties, characterizations, validation testing, different estimation methods. Statistics, Optimization & Information Computing, forthcoming.
- Yousof, H. M. and Korkmaz, M. C. (2017). Topp-Leone Nadarajah-Haghighi distribution: mathematical properties and applications, International Journal of Applied Mathematics. Journal of Statisticians: Statistics and Actuarial Sciences, 2, 119-128.
- Yousof, H. M., Korkmaz, M. C. Hamedani G. G. (2017). The odd Lindley Nadarajah- Haghighi distribution. J. Math. Comput. Sci., 7, 864-882.