Multivariate semi-logistic distributions

作者：Yeh Hsiaw Chan^*

来源：Journal of Multivariate Analysis, 2010, 101(4): 893-908.

DOI：10.1016/j.jmva.2009.09.002

• Multivariate semi-logistic distributions, MSL(1), MSL(2), GMSL
• Multivariate logistic distribution, ML
• Characterizations
• Geometric maximization
• Geometric minimization
• Double arrays
• Multiple logistic regression
• Logit

Three new multivariate semi-logistic distributions (denoted by MSL(1), MSL(2), and GMSL respectively) are studied in this paper. They are more general than Gumbel's (1961) [1] and Arnold's (1992) [2] multivariate logistic distributions. They may serve as competitors to these commonly used multivariate logistic distributions. Various characterization theorems via geometric maximization and geometric minimization procedures of the three MSL(1), MSL(2) and GMSL are proved. The particular multivariate logistic distribution used in the multiple logistic regression model is introduced. Its characterization theorem is also studied. Finally, some further research work on these MSL is also presented. Some probability density plots and contours of the bivariate MSL(1), MSL(2) as well as Gumbel's and Arnold's bivariate logistic distributions are presented in the Appendix.

• 出版日期2010-4