Recurrence relations for bivariate t and extended skew-t distributions and an application to order statistics from bivariate t

In this paper, we derive recurrence relations for cumulative distribution functions (cdf’s) of bivariate t and extended skew-t distributions. These recurrence relations are over ν (the degrees of freedom), and starting from the known results for ν=1 and ν=2, they will allow for the recursive evaluation of the distribution function for any other positive integral value of ν. Then, we consider a linear combination of order statistics from a …