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Multivariate semi-logistic distributions

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  • Yeh, Hsiaw-Chan

Abstract

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.

Suggested Citation

  • Yeh, Hsiaw-Chan, 2010. "Multivariate semi-logistic distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 893-908, April.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:893-908
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    References listed on IDEAS

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    1. Yeh, Hsiaw-Chan, 2007. "Three general multivariate semi-Pareto distributions and their characterizations," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1305-1319, July.
    2. Yeh, Hsiaw-Chan, 2009. "Multivariate semi-Weibull distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1634-1644, September.
    3. Yeh, Hsiaw-Chan, 2004. "Some properties and characterizations for generalized multivariate Pareto distributions," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 47-60, January.
    4. Alice Thomas & K.K. Jose, 2004. "Bivariate semi-Pareto minification processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(3), pages 305-313, June.
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    Cited by:

    1. Yeh, Hsiaw-Chan, 2011. "A multivariate semi-logistic autoregressive process and its characterization," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1370-1379, September.
    2. Yanlai Song & Stanford Shateyi & Jianying He & Xueqing Cui, 2022. "Interactions of Logistic Distribution to Credit Valuation Adjustment: A Study on the Associated Expected Exposure and the Conditional Value at Risk," Mathematics, MDPI, vol. 10(20), pages 1-15, October.

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