Article Sidebar

Download
PDF
Statistic
Read Counter : 731 Download : 527

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

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.

Keywords

Barzilai-Borwein Bagdonavičius-Nikulin Right Censored Validation Goodness-of-fit Test Simulation

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following License

CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

How to Cite
M. Yousof, H., Al-nefaie, A. H., Aidi, K., Ali, M. M., & Mohamed, M. ibrahim. (2021). A Modified Chi-square Type Test for Distributional Validity with Applications to Right Censored Reliability and Medical Data: A Modified Chi-square Type Test. Pakistan Journal of Statistics and Operation Research, 17(4), 1113-1121. https://doi.org/10.18187/pjsor.v17i4.3899
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. 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.
  2. 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€
  3. 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.
  4. 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€
  5. 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€
  6. 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.
  7. BagdonaviÄius, V.; Nikulin, M. (2011a). Chi-squared Goodness-of-fit test for right censored Data. Int. J. Appl. Math. Stat., 24, 30-50.
  8. 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.
  9. Crowder, M. J., Kimber A. C., Smith R. L and Sweeting, T. J. (1991). Statistical analysis of reliability data, CHAPMAN &HALL/CRC
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. Habib, M.G.; Thomas, D.R. (1986). Chi-squared goodness-of-fit tests for randomly censored Data. Ann. Stat, 14, 759-765.
  19. Hollander, M.; Pena, E. (1992). Chi-square goodness-of-fit test for randomly censored data. JASA, 87, 458-463.
  20. 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.
  21. 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.
  22. 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€
  23. 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€
  24. John, P. Klein, Melvin L. Moeschberger (1997). Survival Analysis: Techniques for Censored and Truncated Data, Statistics for Biology and Health.
  25. 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.
  26. 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.
  27. 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€
  28. 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
  29. 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€
  30. 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€
  31. 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.
  32. 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€
  33. Nadarajah, S.and Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45, 543--558.
  34. 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.
  35. 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.
  36. 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).
  37. 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€
  38. 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.
  39. 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€
  40. 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.
  41. 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.
  42. 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.
  43. 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.
  44. 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.
  45. Yousof, H. M., Korkmaz, M. C. Hamedani G. G. (2017). The odd Lindley Nadarajah- Haghighi distribution. J. Math. Comput. Sci., 7, 864-882.

Most read articles by the same author(s)

> >>