Article Sidebar

Download
PDF
Statistic
Read Counter : 673 Download : 609

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract

A new modified version of the BagdonaviÄius-Nikulin goodness-of-fit test statistic is presented for validity for the right censor case under the double Burr type X distribution. The maximum likelihood estimation method in censored data case is used and applied. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right censored estimation method. Another simulation study is presented for testing the null hypothesis under the modified version of the BagdonaviÄius and Nikulin goodness-of-fit statistical test. Four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation.

Keywords

Right Censored Validation Barzilai-Borwein Bagdonavičius-Nikulin Double Burr type X 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
Aidi, K., Butt, N. S., Ali, M. M., Ibrahim, M., Yousof, H. M., & 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. https://doi.org/10.18187/pjsor.v17i3.3888
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Abouelmagd, T. H. M., Hamed, M. S. and Yousof, H. M. (2019). Poisson Burr X Weibull distribution. Journal of Nonlinear Sciences & Applications (JNSA), 12(3), 173-183.
  2. Ali, M. M., Yousof, H. M. and Ibrahim, M. (2021a). A new version of the generalized Rayleigh distribution with copula, properties, applications and different methods of estimation. Optimal Decision Making in Operations Research & Statistics: Methodologies and Applications, VOL 1, 1-25.
  3. Ali, M. M., Ibrahim, M. and Yousof, H. M. (2021b). Expanding the Burr X model: properties, copula, real data modeling and different methods of estimation. Optimal Decision Making in Operations Research & Statistics: Methodologies and Applications, VOL 1, 26-49.
  4. Habib, M.G., Thomas, D.R. (1986). Chi-squared Goodness-of-Fit Tests For Randomly Censored Data, Annals of Statistics, 14(2), 759-765.
  5. Hollander, M., Pena, E.(1992). Chi-square goodness-of-fit test for ran-domly censored data. JASA 87(417), 458-463.
  6. Galanova, N. S., Lemeshko, B. Y. and Chimitova, E. V. (2012). Using nonparametric goodness-of-fit tests to validate accelerated failure time models. Optoelectronics, Instrumentation and Data Processing, 48(6), 580-592.
  7. BagdonaviÄius, V., & Nikulin, M. (2011a). Chi-squared tests for general composite hypotheses from censored samples. Comptes Rendus Mathematique, 349(3-4), 219-223.
  8. BagdonaviÄius, V., Nikulin, M.(2011b). Chi-squared Goodness-of-fit Test for Right Censored Data. International Journal of Applied Mathematics and Statistics, 24, 30-50.
  9. BagdonaviÄius, V., Levuliene, R., J., and Nikulin, M., (2013). Chi-squared goodness-of-fit tests for parametric accelerated failure time models, Communications in Statistics- Theory and Methods, 42(15), 2768-2785.
  10. Crowder M. J., Kimber A.C., Smith R. L and Sweeting, T. J. (1991): Statistical analysis of reliability data, CHAPMAN & HALL/CRC.
  11. 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.
  12. Klein J. P. and Moeschberger M. L. (2003). Survival Analysis : Techniques for Censored and Truncated Data, Springer,New York.
  13. Ibrahim. M., Aidi, K., Ali, M. M. and Yousof, H. M. (2021). The Exponential Generalized Log-Logistic Model: BagdonaviÄius-Nikulin test for Validation and Non-Bayesian Estimation Methods. Communications for Statistical Applications and Methods, forthcoming.
  14. Jahanshahi, S.M.A., Yousof, H. M. and Sharma, V. K. (2019). The Burr X Fréchet Model for Extreme Values: Mathematical Properties, Classical Inference and Bayesian Analysis. Pak. J. Stat. Oper. Res., 15(3), 797-818.
  15. Khalil, M. G., Hamedani, G. G. and Yousof, H. M. (2019). The Burr X exponentiated Weibull model: Characterizations, mathematical properties and applications to failure and survival times data. Pakistan Journal of Statistics and Operation Research, 141-160.
  16. 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€
  17. Mansour, M., Rasekhi, M., Ibrahim, M., Aidi, K., Yousof, H. M. and Elrazik, E. A. (2020b). 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€
  18. Sickle-Santanello, B. J., Farrar, W. B., Decenzo, J. F., Keyhani-Rofagha, S., Klein, J, P., Laufman, H. and Toole, R. V. (1988). Technical and statistical improvements for flow cytometric DNA analysis of paraffin-embedded tissue. Cytometry, 9(6), 954-599.
  19. Voinov, V., Nikulin, M., Balakrishnan, N. (2013). Chi-Squared Goodness of Fit Tests with Applications, Academic Press, Elsevier.
  20. 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(3), 288-305.
  21. Yousof, H. M., Aidi, K., Hamedani, G. G. and Ibrahim. M. (2021a). A new parametric lifetime model 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.
  22. Yousof, H. M., Ali, M. M., Aidi, K., Hamedani, G. G. and Ibrahim, M. (2021b). A new lifetime distribution with properties, characterizations, validation testing, different estimation methods. Statistics, Optimization & Information Computing, forthcoming.