'Distribution function of the linear combination of standardized student-t quantiles [duplicate]
Assume to observe 2 quantiles, x and y, associated with the z% probability. These quantiles are generated by 2 non-independent standardized student-t distributions X and Y.
In case of linear combination of x and y with the Correlation matrix, its distribution function is known?
Can I assume any initial condition on x and y in order to have a known distribution function of the linear combination?
Solution 1:[1]
Answers are in McNeil, Frey and Embrechts, "Quantitative Risk Management", Princeton 2005.
Seems that, assuming a student-t multivariate distribution, linear combination of marginals is also standardized student-t.
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