Prediction of Variables Via Their Order Statistics in Bivariate Elliptical Distributions with Application in the Financial Markets

Assuming that (X-1, X-2) has a bivariate elliptical distribution, we obtain an exact expression for the joint probability density function (pdf) as well as the corresponding conditional pdfs of X-1 and X-(2) := max{X-1, X-2}. The problem is motivated by an application in financial markets. Exchangeable random variables are discussed in more detail. Two special cases of the elliptical distributions that is the normal and the student's t models are investigated. For illustrative purposes, a real data set on the total personal income in California and New York is analyzed using the results obtained. Finally, some concluding remarks and further works are discussed.