Construction of Statistic Distribution Models for Nonparametric Goodness-of-Fit Tests in Testing Composite Hypotheses: The Computer Approach

References

• Anderson, T. W. and Darling, D. A. (1952). Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193–212.
   Google Scholar
• Anderson, T. W. and Darling, D. A. (1954). A test of goodness of fit. Journal of the American Statistical Association, 29, 765–769.
   Google Scholar
• Bolshev, L. N. (1987). On the question on testing some composite statistical hypotheses. In Theory of Probability and Mathematical Statistics. Selected Works, Nauka, Moscow, 5–63.
   Google Scholar
• Bolshev, L. N. and Smirnov, N. V. (1983). Tables of Mathematical Statistics. Moscow: Science. (in Russian)
   Google Scholar
• Chandra, M., Singpurwalla, N. D. and Stephens, M. A. (1981). Statistics for test of fit for the extreme-value and Weibull distribution. Journal of the American Statistical Association, 76(375), 729–731.
   Google Scholar
• Darling, D. A. (1955). The Cramer-Smirnov test in the parametric case. Annals of Mathematical Statistics, 26, 1–20.
   Google Scholar
• Darling, D. A. (1957). The Cramer-Smirnov test in the parametric case. Annals of Mathematical Statistics, 28, 823–838.
   Google Scholar
• Durbin, J. (1973). Weak convergence of the sample distribution function when parameters are estimated. Annals of Mathematical Statistics, 1, 279–290.
   Google Scholar
• Durbin, J. (1975). Kolmogorov-Smirnov tests when parameters are estimated with applications to tests of exponentiality and tests of spacings. Biometrika, 62, 5–22.
   Google Scholar
• Durbin, J. (1976). Kolmogorov-Smirnov test when parameters are estimated. Lecture Notes in Mathematics, 566, 33–44.
   Google Scholar
• Dzhaparidze, K. O. and Nikulin, M. S. (1982). Probability distribution of the Kolmogorov and omega-square statistics for continuous distributions with shift and scale parameters. Journal of Soviet Mathematics, 20, 2147–2163.
   Google Scholar
• Gihman, I. I. (1953).Some remarks on the consistency criterion of A.N. Kolmogorov. Doklady Akademii nauk SSSR, 91(4), 715–718.
   Google Scholar
• Gihman, I. I. (1961). On the empirical distribution function in the case of grouping data. In Selected Translations in Mathematical Statistics and Probability, Vol. 1, American Math. Soc., Providence, RI, 77–81.
   Google Scholar
• Kac, M., Kiefer, J. and Wolfowitz, J. (1955). On Tests of Normality and Other Tests of Goodness of Fit Based on Distance Methods. Annals of Mathematical Statistics, 26, 189–211.
   Google Scholar
• Lemeshko, B. Yu. and Postovalov, S. N. (1998). Statistical distributions of nonparametric goodness-of-fit tests as estimated by the sample parameters of experimentally observed laws. Industrial laboratory, 64(3), 197–208.
   Google Scholar
• Lemeshko, B. Yu. and Postovalov, S. N. (2001). Application of the nonparametric goodness-of-fit tests in testing composite hypotheses. Optoelectronics, Instrumentation and Data Processing, 37(2), 76–88.
   Google Scholar
• Lemeshko, B. Yu. and Postovalov, S. N. (2002). The nonparametric goodness-of-fit tests about fit with Johnson distributions in testing composite hypotheses. Doklady Akademii Nauk Visshei Shkoly, 1(5), 65–74. (in Russian)
   Google Scholar
• Lemeshko, B. Yu. and Maklakov, A. A. (2004). Nonparametric test in testing composite hypotheses on goodness of fit exponential family distributions. Optoelectronics, Instrumentation and Data Processing, 40(3), 3–18.
   Google Scholar
• Lemeshko, B. Yu., Lemeshko, S. B. and Postovalov, S. N. (2007). The power of goodness-of-fit tests for close alternatives. Measurement Techniques, 50(2), 132–141.
   Google Scholar
• Lemeshko, B. Yu., Lemeshko, S. B. and Postovalov, S.N. (2010). Statistic distribution models for some nonparametric goodness-of-fit tests in testing composite hypotheses. Communications in Statistics — Theory and Methods, 39(3), 460–471.
   Google Scholar
• Lemeshko, B. Yu., Lemeshko, S. B. and Postovalov, S.N. (2009). Comparative analysis of the power of goodness-of-fit tests for near competing hypotheses. I. The verification of simple hypotheses. Journal of Applied and Industrial Mathematics, 3(4), 462–475.
   Google Scholar
• Lemeshko, B. Yu., Lemeshko, S. B. and Postovalov, S.N. (2010). Comparative analysis of the power of goodness-of-fit tests for near competing hypotheses. II. The verification of complex hypotheses. Journal of Applied and Industrial Mathematics, 4(1), 79–93.
   Google Scholar
• Lemeshko, B. Yu. and Lemeshko, S. B. (2007). Statistic distributions of the nonparametric goodness-of-fit tests in testing hypotheses relative to beta-distributions. Doklady Akademii Nauk Visshei Shkoly, 2(9), 6–16. (in Russian)
   Google Scholar
• Lemeshko, B. Yu. and Lemeshko, S. B. (2009). Distribution models for nonparametric tests for fit in verifying complicated hypotheses and maximum-likelihood estimators. Part 1. Measurement Techniques, 52(6), 555–565.
   Google Scholar
• Lemeshko, B. Yu. and Lemeshko, S. B. (2009). Models for statistical distributions in nonparametric fitting tests on composite hypotheses based on maximum-likelihood estimators. Part II. Measurement Techniques, 52(8), 799–812.
   Google Scholar
• Lemeshko, B. Yu., Lemeshko, S. B., Akushkina, K. A., Nikulin, M. S. and Saaidia, Noureddine. (2011). Inverse Gaussian model and its applications in reliability and survival analysis. In Mathematical and Statistical Models and Methods in Reliability. Applications to Medicine, Finance, and Quality Control, edited by V. Rykov, N. Balakrishnan and M. Nikulin, 433–453, Birkhauser, Boston.
   Google Scholar
• Lemeshko, B. Yu., Lemeshko, S. B., Chimitova, E. V., Postovalov, S. N. and Rogozhnikov, A. P. (2011). Software system for simulation and research of probabilistic regularities and statistical data analysis in reliability and quality control. In Mathematical and Statistical Models and Methods in Reliability. Applications to Medicine, Finance, and Quality Control, edited by V. Rykov, N. Balakrishnan and M. Nikulin, 417–432, Birkhauser, Boston.
   Google Scholar
• Lemeshko, B. Yu., Lemeshko, S. B., Nikulin, M. S. and Saaidia, N. (2010). Modeling statistic distributions for nonparametric goodness-of-fit criteria for testing complex hypotheses with respect to the inverse Gaussian law. Automation and Remote Control, 71(7), 1358–1373.
   Google Scholar
• Lemeshko, S. B. (2007). Expansion of Applied Opportunities of Some Classical Methods of Mathematical Statistics. The dissertation on competition of a scientific degree of Cand. Tech. Sci., Novosibirsk State Technical University, Novosibirsk. (in Russian)
   Google Scholar
• Martinov, G. V. (1978). Omega-Square Tests. Moscow: Science. (in Russian)
   Google Scholar
• Nikulin, M. S. (1973). About chi-square goodness-of-fit test for continuous distributions. Teoriya Veroyatnostei i ee Primeneniya, 18(3), 675–676.
   Google Scholar
• Nikulin, M. S. (1973). Chi-Square Test for Continuous Distributions with Shift and Scale Parameters. Teoriya Veroyatnostei i ee Primeneniya, 18(3), 583–592.
   Google Scholar
• Nikulin, M. S. (1992). Gihman and goodness-of-fit tests for grouped data. Mathematical Reports of the Academy of Science of the Royal Society of Canada, 14(4), 151–156.
   Google Scholar
• Nikulin, M. S. (1992). A variant of the generalized omega-square statistic. Journal of Soviet Mathematics, 61 (4), 1896–1900, translation from Zapiski nauchnikh seminarov LOMI, (1989), 177, 108–113.
   Google Scholar
• Pearson, E. S. and Hartley, H. O. (1972). Biometrica Tables for Statistics. Volume 2. Cambridge: University Press.
   Google Scholar
• R 50.1.037–2002. (2002). Recommendations for Standardization. Applied statistics. Rules of Check of Experimental and Theoretical Distribution of the Consent. Part II. Nonparametric Goodness-of-Fit Test. Moscow: Publishing house of the standards. (in Russian)
   Google Scholar
• Rao, K. C. and Robson, D. S. (1974). A chi-squared statistic for goodness-of-fit tests within the exponential family. Communications in Statistics, 3, 1139–1153.
   Google Scholar
• Stephens, M. A. (1970). Use of Kolmogorov-Smirnov, Cramer-von Mises and related statistics-without extensive table. Journal of the Royal Statistical Society, 32, 115–122.
   Google Scholar
• Stephens, M. A. (1974). EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, 730–737.
   Google Scholar
• Tyurin, Yu. N. (1984). On the limiting Kolmogorov-Smirnov statistic distribution for composite hypothesis. Doklady Akademii Nauk SSSR. Ser. Math., 48(6), 1314–1343. (in Russian)
   Google Scholar
• Tyurin, Yu. N. and Savvushkina, N. E. (1984). Goodness-of-fit test for Weibull-Gnedenko distribution. Doklady Akademii Nauk SSSR. Ser. Techn. Cybernetica, 3, 109–112. (in Russian)
   Google Scholar