On moments of doubly truncated multivariate normal mean–variance mixture distributions with application to multivariate tail conditional expectation

2020 ◽  
Vol 177 ◽  
pp. 104586
Author(s):  
Roohollah Roozegar ◽  
Narayanaswamy Balakrishnan ◽  
Ahad Jamalizadeh
Keyword(s):  
Conditional Expectation ◽  
Mixture Distributions ◽  
Multivariate Normal ◽  
Tail Conditional Expectation ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Mean Variance

scholarly journals Integral stochastic ordering of the multivariate normal mean-variance and the skew-normal scale-shape mixture models

2020 ◽  
Vol 8 (1) ◽  
pp. 1-16
Author(s):  
Dariush Jamali ◽  
Mehdi Amiri ◽  
Ahad Jamalizadeh ◽  
N. Balakrishnan
Keyword(s):  
Sufficient Conditions ◽  
Stochastic Ordering ◽  
Multivariate Normal ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Stop Loss ◽  
Necessary And Sufficient ◽  
Mean Variance ◽  
Normal Scale ◽  
Skew Normal

‎In this paper‎, ‎we introduce integral stochastic ordering of two‎ most important classes of distributions that are commonly used to fit data possessing high values of skewness and (or)‎ ‎kurtosis‎. ‎The first one is based on the selection distributions started by the univariate skew-normal distribution‎. ‎A broad‎, ‎flexible and newest class in this area is the scale and shape mixture of multivariate skew-normal distributions‎. ‎The second one is the general class of Normal Mean-Variance Mixture distributions‎. ‎We then derive necessary and sufficient conditions for comparing the random vectors from these two classes of distributions‎. ‎The integral orders considered here are the usual‎, ‎concordance‎, ‎supermodular‎, ‎convex‎, ‎increasing convex and directionally convex stochastic orders‎. ‎Moreover‎, ‎for bivariate random vectors‎, ‎in the sense of stop-loss and bivariate concordance stochastic orders‎, ‎the dependence strength of random portfolios is characterized in terms of order of correlations‎.

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