On Extremes of Two-Dimensional Student-t Distribution of the Marshall–Olkin Type

Although there are some results related to classical bivariate Student- t distribution, studying the exact distribution of its extremes is not so easy. However, the extreme values of a bivariate Student- t distribution may play an important role in both statistical theory and practice. Therefore, this manuscript represents a pioneer work related to the studying extreme values of the bivariate Student- t distribution. For this reason, we consider another two-dimensional Student- t distribution, which is defined using the Marshall–Olkin approach. The difficulty in obtaining nice expressions for the exact distribution of the extremes for bivariate Student- t distribution may be solved by studying a more friendly distribution. The Marshall–Olkin approach is a good choice since it naturally involves extremes of the random variables. Therefore, this is one of the motivation for studying bivariate Student- t distribution of the Marshall Olkin (MO) type. Then, we study the distribution of the extremes M = min { X 1 , X 2 } and S = max { X 1 , X 2 } , where random vector ( X 1 , X 2 ) is from bivariate MO Student- t distribution. We obtain the moments and compute the percentiles of the distributions.