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Research Article

A new Kolmogorov-Smirnov test based on representative points in the exponential distribution family

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Received 19 Dec 2023, Accepted 20 Jul 2024, Published online: 04 Aug 2024

References

  • Kallioras AG, Koutrouvelis IA, Canavos GC. Testing the fit of gamma distributions using the empirical moment generating function. Commun Stat Theory Methods. 2006;35(3):527–540. doi: 10.1080/03610920500476424
  • Nikulin M, Voinov V. A chi-square goodness-of-fit test for exponential distributions of the first order. In: Stability Problems for Stochastic Models: Proceedings of the 11th International Seminar Held in Sukhumi (Abkhazian Autonomous Republic) USSR, Sept. 25–Oct. 1, 1987. Springer; 2006. p. 239–258.
  • Henze N, Meintanis SG, Ebner B. Goodness-of-fit tests for the gamma distribution based on the empirical laplace transform. Commun Stat Theory Methods. 2012;41(9):1543–1556. doi: 10.1080/03610926.2010.542851
  • Wang S, Liang J, Zhou M, et al. Testing multivariate normality based on f-representative points. Mathematics. 2022;10(22):4300. doi: 10.3390/math10224300
  • Cox DR. Note on grouping. J Am Stat Assoc. 1957;52(280):543–547. doi: 10.1080/01621459.1957.10501411
  • Flury BA. Principal points. Biometrika. 1990;77(1):33–41. doi: 10.1093/biomet/77.1.33
  • Fang K-T, Wang Y. Number-theoretic methods in statistics. Vol. 51. London (UK): CRC Press; 1993.
  • Pagès G. Introduction to vector quantization and its applications for numerics. ESAIM: Proc Surveys. 2015;48:29–79. doi: 10.1051/proc/201448002
  • Tarpey T. Self-consistency algorithms. J Comput Graph Stat. 1999;8(4):889–905. doi: 10.1080/10618600.1999.10474854
  • Fang K-T, Pan J. A review of representative points of statistical distributions and their applications. Mathematics. 2023;11(13):2930. doi: 10.3390/math11132930
  • Fang K-T. Application of the theory of the conditional distribution for the standardization of clothes. Acta Math Appl Sin. 1976;2:62–74.
  • Pham H, Printems J. Optimal quantization methods and applications to numerical problems in finance. Berlin (Germany): HAL; 2004.
  • Pagès G, Printems J. Optimal quadratic quantization for numerics: the gaussian case. Monte Carlo Methods Appl. 2003;9:135–165. doi: 10.1515/156939603322663321
  • Fang K-T, Zhou M, Wang W. Applications of the representative points in statistical simulations. Sci China Math. 2014;57:2609–2620. doi: 10.1007/s11425-014-4860-9
  • Li Y, Fang K-T, He P, et al. Representative points from a mixture of two normal distributions. Mathematics. 2022;10(21):3952. doi: 10.3390/math10213952
  • Edgeman RL, Scott RC, Pavur RJ. A modified kolmogorov-smirnov test for the inverse gaussian density with unknown parameters. Commun Stat Simul Comput. 1988;17(4):1203–1212. doi: 10.1080/03610918808812721
  • Lilliefors HW. On the kolmogorov-smirnov test for the exponential distribution with mean unknown. J Am Stat Assoc. 1969;64(325):387–389. doi: 10.1080/01621459.1969.10500983
  • Woodruff BW, Viviano PJ, Moore AH, et al. Modified goodness-of-fit tests for gamma distributions with unknown location and scale parameters. IEEE Trans Reliab. 1984;R-33(3):241–245. doi: 10.1109/TR.1984.5221801
  • Tadikamalla PR. Kolmogorov-smirnov type test-statistics for the gamma, erlang-2 and the inverse gaussian distributions when the parameters are unknown. Commun Stat Simul Comput. 1990;19(1):305–314. doi: 10.1080/03610919008812858
  • Ke X, Wang S, Zhou M, et al. New approaches on parameter estimation of the gamma distribution. Mathematics. 2023;11(4):927. doi: 10.3390/math11040927
  • Berman M. The maximum likelihood estimators of the parameters of the gamma distribution are always positively biased. Commun Stat Theory Methods. 1981;10(7):693–697. doi: 10.1080/03610928108828067
  • Bowman K, Shenton L. Problems with maximum likelihood estimation and the 3 parameter gamma distribution. J Stat Comput Simul. 2002;72(5):391–401. doi: 10.1080/00949650213534
  • Mazucheli J, Menezes AFB, Dey S. Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution. Commun Stat Theory Methods. 2018;47(15):3767–3778. doi: 10.1080/03610926.2017.1361993
  • Li Y, Fang K-T. A new approach to parameter estimation of mixture of two normal distributions. Commun Stat Simul Comput. 2022;53:1–13. doi: 10.1080/03610918.2022.2112054
  • Harrell FE, Davis C. A new distribution-free quantile estimator. Biometrika. 1982;69(3):635–640. doi: 10.1093/biomet/69.3.635
  • Gail MH, Green SB. Critical values for the one-sided two-sample kolmogorov-smirnov statistic. J Am Stat Assoc. 1976;71(355):757–760. doi: 10.1080/01621459.1976.10481562
  • Henze N. Empirical-distribution-function goodness-of-fit tests for discrete models. Can J Stat. 1996;24(1):81–93. doi: 10.2307/3315691
  • Takacs L. On the comparison of two empirical distribution functions. Ann Math Stat. 1971;42(4):1157–1166. doi: 10.1214/aoms/1177693232
  • Kolmogorov AN. Sulla determinazione empirica di una legge didistribuzione. Giorn Dell'inst Ital Degli Att. 1933;4:89–91.
  • Doob JL. Heuristic approach to the kolmogorov-smirnov theorems. Ann Math Stat. 1949;20:393–403. doi: 10.1214/aoms/1177729991
  • Feller W. On the kolmogorov-smirnov limit theorems for empirical distributions. Ann Math Stat. 1948;19(2):177–189. doi: 10.1214/aoms/1177730243
  • Massey Jr FJ. The kolmogorov-smirnov test for goodness of fit. J Am Stat Assoc. 1951;46(253):68–78. doi: 10.1080/01621459.1951.10500769
  • Smirnov NV. On the estimation of the discrepancy between empirical curves of distribution for two independent samples. Bull Math Univ Moscou. 1939;2(2):3–14.
  • Glivenko V. Sulla determinazione empirica delle leggi di probabilita. Gion Ist Ital Attauri. 1933;4:92–99.
  • Fei R. Statistical relationship between the representative points and the population. J Wuxi Inst Light Ind. 1991;10:78–81.
  • Graf S, Luschgy H. Foundations of quantization for probability distributions. Berlin (Germany): Springer; 2007.
  • Proschan F. Theoretical explanation of observed decreasing failure rate. Technometrics. 1963;5(3):375–383. doi: 10.1080/00401706.1963.10490105
  • Keating JP, Glaser RE, Ketchum NS. Testing hypotheses about the shape parameter of a gamma distribution. Technometrics. 1990;32(1):67–82. doi: 10.1080/00401706.1990.10484594
  • Pal N, Jin C, Lim WK. Handbook of exponential and related distributions for engineers and scientists. London (UK): CRC Press; 2005.
  • Bhaumik DK, Kapur K, Gibbons RD. Testing parameters of a gamma distribution for small samples. Technometrics. 2009;51(3):326–334. doi: 10.1198/tech.2009.07038
  • Lee ET, Wang J. Statistical methods for survival data analysis. Vol. 476. New York (US): John Wiley & Sons; 2003.
  • Ozonur D, Paul S. Goodness of fit tests of the two-parameter gamma distribution against the three-parameter generalized gamma distribution. Commun Stat Simul Comput. 2020;51(3):687–697. doi: 10.1080/03610918.2020.1729807

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