In order to improve the fitting accuracy of college
students’ test scores, this paper proposes two-component mixed generalized
normal distribution, uses maximum likelihood estimation method and Expectation
Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct
numerical simulation, and performs fitting analysis on the test scores of
Linear Algebra and Advanced Mathematics of F University. The empirical results
show that the two-component mixed generalized normal distribution is better
than the commonly used two-component mixed normal distribution in fitting
college students’ test data, and has good application value.
References
[1]
Li, L. and Zhang, W.H. (2021) Analysis on Normal Distribution of College Course Examination Results. China Exam, 4, 86-93.
[2]
Yin, X.F. (2007) Fitting the Distribution of College Students’ Test Scores Based on Mixed Normal Distribution. Statistics and Decision Making, 8, 133-135.
[3]
Gu, C.C. and Chi, Z.Y. (2010) Research on the Distribution Law of Students’ Achievements. Journal of Anyang Institute of Technology, 9, 88-90.
[4]
Zhang, J.J. and Ma, D.J. (2021) Analysis of Mixed Normal Distribution of Test Results. Mathematical Statistics and Management, 40, 815-821.
[5]
Wen, L.L., Qiu, Y.J., Wang, M.H., Yin, J.L. and Chen, P.Y. (2022) Numerical Characteristics and Parameter Estimation of Finite Mixed Generalized Normal Distribution. Communications in Statistics—Simulation and Computation, 51, 3596-3620. https://doi.org/10.1080/03610918.2020.1720733
[6]
Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977) Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39, 1-22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
[7]
Meng, X.L. and Rubin, D.B. (1993) Maximum Likelihood Estimation via the ECM Algorithm: A General Framework. Biometrika, 80, 267-278. https://doi.org/10.1093/biomet/80.2.267
[8]
Chen, Y., Fei, Y. and Pan, J.X. (2015) Statistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of Non-Normal Random Effects. Open Journal of Statistics, 5, 568-584. https://doi.org/10.4236/ojs.2015.56059
[9]
Newey, W.K. and McFadden, D. (1994) Large Sample Estimation and Hypothesis Testing. Handbook of Econometrics, 4, 2111-2245. https://doi.org/10.1016/S1573-4412(05)80005-4
[10]
Redner, R.A. and Walker, H.F. (1984) Mixture Densities, Maximum Likelihood and the EM Algorithm. SIAM Review, 26, 195-239. https://doi.org/10.1137/1026034
[11]
McLachlan, G. J. and Peel, D. (2004) Finite Mixture Models. John Wiley & Sons, New York.
[12]
Tadikamalla, P. (1980) Random Sampling from the Exponential Power Distribution. Journal of the American Statistical Association, 75, 683-686. https://doi.org/10.1080/01621459.1980.10477533
[13]
Chiodi, M. (1995) Generation of Pseudo-Random Variates from a Normal Distribution of Order P. Italian Journal of Applied Statistics, 7, 401-416.
[14]
Huang, G.J., Ou, S.D. and Li, Q. (2019) Estimation of Failure Rate of College Mathematics Examination and Statistical Analysis of Its Influencing Factors. Journal of Guangxi University: Natural Science Edition, 44, 1835-1841.
