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 Conditiona...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.展开更多
This paper presents an extension of the factor analysis model based on the normal mean-variance mixture of the Birnbaum-Saunders in the presence of nonresponses and missing data.This model can be used as a powerful to...This paper presents an extension of the factor analysis model based on the normal mean-variance mixture of the Birnbaum-Saunders in the presence of nonresponses and missing data.This model can be used as a powerful tool to model non-normal features observed from data such as strongly skewed and heavy-tailed noises.Missing data may occur due to operator error or incomplete data capturing therefore cannot be ignored in factor analysis modeling.We implement an EM-type algorithm for maximum likelihood estimation and propose single imputation of possible missing values under a missing at random mechanism.The potential and applicability of our proposed method are illustrated through analyzing both simulated and real datasets.展开更多
文摘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.
基金This work was based on research supported by the National Research Foundation,South Africa(SRUG190308422768 Grant No.120839 and IFR170227223754 Grant No.109214)the South African NRF SARChI Research Chair in Computational and Methodological Statistics(UID:71199)The research of the corresponding author is supported by a grant from Ferdowsi University of Mashhad(N.2/54034).
文摘This paper presents an extension of the factor analysis model based on the normal mean-variance mixture of the Birnbaum-Saunders in the presence of nonresponses and missing data.This model can be used as a powerful tool to model non-normal features observed from data such as strongly skewed and heavy-tailed noises.Missing data may occur due to operator error or incomplete data capturing therefore cannot be ignored in factor analysis modeling.We implement an EM-type algorithm for maximum likelihood estimation and propose single imputation of possible missing values under a missing at random mechanism.The potential and applicability of our proposed method are illustrated through analyzing both simulated and real datasets.
