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AIMS Mathematics

2022, Volume 7, Issue 8: 13733-13745. doi: 10.3934/math.2022756
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Research article

Non-parametric hypothesis testing to model some cancers based on goodness of fit

  • Department of Statistics and Operation Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
  • Received: 02 February 2022 Revised: 03 May 2022 Accepted: 05 May 2022 Published: 23 May 2022

  • MSC : 62G10, 62G20, 62N05

  • By observing the failure behavior of the recorded survival data, we aim to compare the different processing approaches or the effectiveness of the devices or systems applied in this non-parametric statistical test. We'll apply the proposed strategy of used better than aged in Laplace (UBAL) transform order, which assumes that the data used in the test will either behave as UBAL Property or exponential behavior. If the survival data is UBAL, it means that the suggested treatment strategy is effective, whereas if the data is exponential, the recommended treatment strategy has no negative or positive effect on patients, as indicated in the application section. To guarantee the test's validity, we calculated the suggested test's power in both censored and uncensored data, as well as its efficiency, compared the results to other tests, and then applied the test to a variety of real data.

    Citation: M. E. Bakr, M. Nagy, Abdulhakim A. Al-Babtain. Non-parametric hypothesis testing to model some cancers based on goodness of fit[J]. AIMS Mathematics, 2022, 7(8): 13733-13745. doi: 10.3934/math.2022756

    Related Papers:

  • By observing the failure behavior of the recorded survival data, we aim to compare the different processing approaches or the effectiveness of the devices or systems applied in this non-parametric statistical test. We'll apply the proposed strategy of used better than aged in Laplace (UBAL) transform order, which assumes that the data used in the test will either behave as UBAL Property or exponential behavior. If the survival data is UBAL, it means that the suggested treatment strategy is effective, whereas if the data is exponential, the recommended treatment strategy has no negative or positive effect on patients, as indicated in the application section. To guarantee the test's validity, we calculated the suggested test's power in both censored and uncensored data, as well as its efficiency, compared the results to other tests, and then applied the test to a variety of real data.


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    [1] J. Navarro, F. Pellerey, Preservation of ILR and IFR aging classes in sums of dependent random variables, Appl. Stoch. Models Bus. Ind., 38 (2022), 240-261. https://doi.org/10.1002/asmb.2657 doi: 10.1002/asmb.2657
    [2] M. C. Bryson, M. M. Siddiqui, Some criteria for aging, J. Amer. Stat. Assoc., 64 (1969), 1472-1483. https://doi.org/10.2307/2286084 doi: 10.2307/2286084
    [3] R. E. Barlow, F. Proschan, Statistical theory of reliability and life testing: Probability models, Holt, Rinehart and Winston, 1975.
    [4] J. D. Esary, A. W. Marshall, F. Proschan, Some reliability applications of the hazard transform, SIAM J. Appl. Math., 18 (1970), 849-860.
    [5] J. Navarro, Preservation of DMRL and IMRL aging classes under the formation of order statistics and coherent systems, Stat. Probabil. Lett., 137 (2018), 264-268. https://doi.org/10.1016/j.spl.2018.02.005 doi: 10.1016/j.spl.2018.02.005
    [6] J. Cao, Y. Wang, The NBUC and NWUC classes of life distributions, J. Appl. Probabil., 28 (1991), 473-479. https://doi.org/10.2307/3214882 doi: 10.2307/3214882
    [7] J. M. Fernandez-Ponce, F. Pellerey, M. R. Rodrıguez-Grinolo, On a new NBUE property in multivariate sense: An application, Comput. Stat. Data Anal., 55 (2011), 3283-3294. https://doi.org/10.1016/j.csda.2011.06.010 doi: 10.1016/j.csda.2011.06.010
    [8] I. A. Ahmad, Some properties of classes of life distributions with unknown age, Stat. Probabil. Lett., 69 (2004), 333-342. https://doi.org/10.1016/j.spl.2004.06.029 doi: 10.1016/j.spl.2004.06.029
    [9] S. E. Abu-Youssef, N. S. A. Ali, M. E. Bakr, Non-parametric testing for unknown age (UBAL) class of life distribution, J. Test. Eval., 48 (2019), 4576-4587. https://doi.org/10.1520/JTE20170726 doi: 10.1520/JTE20170726
    [10] S. E. Abu-Youssef, M. E. Bakr, Laplace transform order for unknown age class of life distribution with some applications, J. Stat. Appl. Probabil., 7 (2018), 105-114. http://dx.doi.org/10.18576/jsap/070110 doi: 10.18576/jsap/070110
    [11] J. M. Fernandez-Ponce, M. R. Rodrıguez-Grinolo, Testing exponentiality against NBUE distributions with an application in environmental extremes, Stoch. Environ. Res. Risk Assess., 29 (2015), 679-692. https://doi.org/10.1007/s00477-014-0981-5 doi: 10.1007/s00477-014-0981-5
    [12] M. A. W. Mahmoud, L. S. Diab, D. M. Radi, Testing exponentiality against renewal new better than used in Laplace transform order: Applications in reliability, J. Egypt. Math. Soc., 27 (2019), 49-60. https://doi.org/10.1186/s42787-019-0044-7 doi: 10.1186/s42787-019-0044-7
    [13] S. E. Abu-Youssef, B. I. Mohammed, M. E. Bakr, Nonparametric test for unknown age class of life distributions, Int. J. Reliab. Appl., 15 (2014), 99-110.
    [14] S. E. Abu-Youssef, N. S. A. Ali, M. E. Bakr, Used better than aged in mgf ordering class of life distribution with application of hypothesis testing, J. Stat. Appl. Probabil. Lett., 7 (2020), 23-32. http://dx.doi.org/10.18576/jsapl/070103 doi: 10.18576/jsapl/070103
    [15] A. J. Lee, U-statistics: Theory and practice, 1 Ed., New York: Routledge, 1990. https://doi.org/10.1201/9780203734520
    [16] M. A. W. Mahmoud, A. N. Abdul Alim, A goodness of fit approach to for testing NBUFR (NWUFR) and NBAFR (NWAFR) properties, Int. J. Reliab. Appl., 9 (2008), 125-140.
    [17] A. M. Abouammoh, S. A. Abdulghani, I. S. Qamber, On partial orderings and testing of new better than renewal used classes, Reliab. Eng. Syst. Safe., 43 (1994), 37-41. https://doi.org/10.1016/0951-8320(94)90094-9 doi: 10.1016/0951-8320(94)90094-9
    [18] S. E. Abu-Youssef, S. T. Gerges, Based on the goodness of fit approach, a new test statistic for testing NBUCmgf class of life distributions, Pak. J. Statist., 38 (2022), 129-144.
    [19] K. Abbas, Z. Hussain, N. Rashid, A. Ali, M. Taj, S. A. Khan, et al., Bayesian estimation of Gumbel type-Ⅱ distribution under type-Ⅱ censoring with medical applications, J. Comput. Math. Methods Med., 2020 (2020), 1-11. https://doi.org/10.1155/2020/1876073 doi: 10.1155/2020/1876073
    [20] S. Y. Lee, R. A. Wolfe, A simple test for independent censoring under the proportional hazards model, Biometrics, 54 (1998), 1176-1182. https://doi.org/10.2307/2533867 doi: 10.2307/2533867
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