Chi-squared type test for distributional censored and uncensored validity with numerical assessments and real data applications. (English) Zbl 07887561
Summary: In this work, we introduce a new chi-squared type test the odd Lindley exponentiated gamma distribution. The new test is an extension of the Nikulin-Rao-Robson test. The new test is tailored to fit the right censored data. The performance of the new test, as well as the baseline Nikulin-Rao-Robson test, are evaluated via numerical simulation. The new test, as well as the baseline Nikulin-Rao-Robson test, are also evaluated using the data. Furthermore, we present some characterization results.
MSC:
| 62-XX | Statistics |
Keywords:
chi-square type test; Nikulin-Rao-Robson; right censored data; simulations; testing; validation; characterizationReferences:
| [1] | Abouelmagd, T. H. M., Hamed, M. S., Hamedani, G. G., Ali, M. M., Goual, H., Korkmaz, M. C., & Yousof, H. M. (2019a). The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test. Journal of Nonlinear Sciences and Applications,12(5), 314-336. |
| [2] | Abouelmagd, T. H. M., Hamed, M. S., Handique, L., Goual, H., Ali, M. M., Yousof, H. M., & Korkmaz, M. C. (2019b). A new class of distributions based on the zero truncated Poisson distribution with properties and applications. Journal of Nonlinear Sciences & Applications (JNSA),12(3), 152-164. |
| [3] | Aidi, K., Butt, N. S., Ali, M. M., Ibrahim, M., Yousof, H. M., & Shehata, W. A. (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, 615-623. |
| [4] | Bagdonavičius, V., & Nikulin, M. (2011a). Chi-squared goodness-of-fit test for right censored Data. International Journal of Applied Mathematics and Statistics,24, 30-50. |
| [5] | Bagdonavičius, 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. · Zbl 1209.62227 |
| [6] | Bjerkedal, T., Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli, American Journal of Hygiene, 72, 130-148, 1960 |
| [7] | Crowder, M. J., Kimber, A. C., Smith, R. L., & Sweeting, T. J. (1991). Statistical analysis of reliability data. Chapman & Hall/CRC. |
| [8] | Galanova, N.; Lemeshko, BY; Chimitova, EV, Using nonparametric goodness-of-fit tests to validate accelerated failure time models, Optoelectronics, Instrumentation and Data Processing, 48, 580-592, 2012 · doi:10.3103/S8756699012060064 |
| [9] | Gijbels, I.; Gurler, U., Estimation of a change-point in a hazard function based on censored data, Lifetime Data Analysis, 9, 395-411, 2003 · Zbl 1038.62091 · doi:10.1023/B:LIDA.0000012424.71723.9d |
| [10] | Glänzel, W. (1987). A characterization theorem based on truncated moments and its application to some distribution families. In Mathematical statistics and probability theory (Bad Tatzmannsdorf, 1986) (Vol. B, pp. 75-84). Reidel. · Zbl 0631.62020 |
| [11] | Glänzel, W., Some consequences of a characterization theorem based on truncated moments, Statistics: A Journal of Theoretical and Applied Statistics, 21, 4, 613-618, 1990 · Zbl 0716.62015 · doi:10.1080/02331889008802273 |
| [12] | Gomes-Silva, FS; Percontini, A.; de Brito, E.; Ramos, MW; Venâncio, R.; Cordeiro, GM, The odd Lindley-G family of distributions, Austrian Journal of Statistics, 46, 1, 65-87, 2017 · doi:10.17713/ajs.v46i1.222 |
| [13] | Goual, H.; Yousof, HM, Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test, Journal of Applied Statistics, 47, 3, 393-423, 2020 · Zbl 1521.62338 · doi:10.1080/02664763.2019.1639642 |
| [14] | Goual, H., Yousof, H. M., & 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, 745-771. |
| [15] | Goual, H.; Yousof, HM; Ali, MM, 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, 2020 · doi:10.22436/jnsa.013.06.04 |
| [16] | Gupta, RC; Gupta, PL; Gupta, RD, Modeling failure time data by Lehman alternatives, Communications in Statistics-Theory and Methods, 27, 4, 887-904, 1998 · Zbl 0900.62534 · doi:10.1080/03610929808832134 |
| [17] | Habib, M. G., & Thomas, D. R. (1986). Chi-square goodness-if-fit tests for randomly censored data. The Annals of Statistics, 759-765. · Zbl 0633.62041 |
| [18] | Hamedani, G. G. (2013). On certain generalized gamma convolution distributions II. Technical Report, No. 484, MSCS, Marquette University. |
| [19] | Hollander, M.; Pena, EA, A chi-squared goodness-of-fit test for randomly censored data, Journal of the American Statistical Association, 87, 418, 458-463, 1992 · Zbl 0763.62027 · doi:10.1080/01621459.1992.10475226 |
| [20] | Ibrahim, M.; Aidi, K.; Ali, MM; Yousof, HM, The exponential generalized log-logistic model: Bagdonavičius-Nikulin test for validation and non-Bayesian estimation methods, Communications for Statistical Applications and Methods, 29, 1, 681-705, 2021 · doi:10.29220/CSAM.2022.29.1.681 |
| [21] | Ibrahim, M.; Altun, E.; Goual, H.; Yousof, HM, 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, 2020 |
| [22] | Ibrahim, M.; Yadav, AS; Yousof, HM; Goual, H.; Hamedani, GG, 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, 2019 · doi:10.29220/CSAM.2019.26.5.473 |
| [23] | Mansour, M., Rasekhi, M., Ibrahim, M., Aidi, K., Yousof, H. M., & Elrazik, E. A. (2020a). A new parametric life distribution with modified Bagdonavičius-Nikulin goodness-of-fit test for censored validation, properties, applications, and different estimation methods. Entropy,22(5), 592. |
| [24] | Mansour, M. M., Ibrahim, M., Aidi, K., Shafique Butt, N., Ali, M. M., Yousof, H. M., & Hamed, M. S. (2020b). 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. |
| [25] | Murthy, D. N. P., Xie, M., & Jiang, R. (2004). Weibull models. Wiley. · Zbl 1047.62095 |
| [26] | Nigm, AM; AL-Hussaini, EK; Jaheen, ZF, Bayesian one-sample prediction of future observations under Pareto distribution, Statistics, 37, 6, 527-536, 2003 · Zbl 1032.62025 · doi:10.1080/02331880310001598837 |
| [27] | Nikulin, M. (1973a). Chi-squared test for normality. In Proceedings of the international vilnius conference on probability theory and mathematical statistics (Vol. 2, No. 1, pp. 119-122). Vilnius, Lithuania: Vilnius University. |
| [28] | Nikulin, M. S. (1973b). Chi-squared test for continuous distributions with shift and scale parameters. Theory of Probability and its Applications,18, 559-568. · Zbl 0302.62022 |
| [29] | Nikulin, M. S. (1973c). On a chi-squared test for continuous distributions. Theory of Probability and its Applications,19, 638-639. |
| [30] | Rao, KC; Robson, DS, A chi-square statistic for goodness-of-fit tests within the exponential family, Communication in Statistics, 3, 1139-1153, 1974 · Zbl 0294.62057 · doi:10.1080/03610927408827216 |
| [31] | Ravi, V.; Gilbert, PD, BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function, Journal of Statistical Software, 32, 4, 1-26, 2009 |
| [32] | Sickle-Santanello, BJ; Farrar, WB; Decenzo, JF; Keyhani-Rofagha, S.; Klein, J.; Pearl, D.; O’Toole, RV, Technical and statistical improvements for flow cytometric DNA analysis of paraffin-embedded tissue, Cytometry: The Journal of the International Society for Analytical Cytology, 9, 6, 594-599, 1988 · doi:10.1002/cyto.990090613 |
| [33] | Voinov, V., Nikulin, M., & Balakrishnan, N. (2013). Chi-squared goodness of fit tests with applications. Academic Press, Elsevier. · Zbl 1276.62027 |
| [34] | Woolson, RF; Tsuang, MT; Simpson, JC, An evaluation of the Feighner criteria for schizophrenia and affective disorders using long-term outcome data, Psychological Medicine, 11, 2, 281-287, 1981 · doi:10.1017/S0033291700052107 |
| [35] | Yadav, AS; Goual, H.; Alotaibi, RM; Ali, MM; Yousof, HM, 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, 2019 · doi:10.3390/sym12010057 |
| [36] | Yadav, AS; Shukla, S.; Goual, H.; Saha, M.; Yousof, HM, Validation of Xgamma exponential model via Nikulin-Rao-Robson goodness-of-fit-test under complete and censored sample with different methods of estimation, Statistics, Optimization & Information Computing, 10, 2, 457-483, 2022 · doi:10.19139/soic-2310-5070-1107 |
| [37] | Yousof, H. M., Aidi, K., Hamedani, G., & 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. |
| [38] | Yousof, H. M., Al-nefaie, A. H., Aidi, K., Ali, M. M., & Ibrahim Mohamed, M. (2021b). A modified chi-square type test for distributional validity with applications to right censored reliability and medical data. Pakistan Journal of Statistics and Operation Research,17(4), 1113-1121. |
| [39] | Yousof, H. M., Ali, M. M., Goual, H., & Ibrahim, M. (2021c). A new reciprocal Rayleigh extension: Properties, copulas, different methods of estimation and a modified right-censored test for validation. Statistics in Transition New Series,22(3), 99-121. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
