二元分布函数的密度收敛

Density Convergence of 2-Dimensional Distributions

设 { ( Xi,Yi) ,i≥ 1 }是独立同分布二维随机向量列 ,其共同分布函数为 F.设 F属于 G的吸引场 ,本文假定边缘分布满足 Von-Mises条件 ,主要考虑二维极大值向量 Mn 密度收敛局部一致成立的问题 .本文将 Resnick[3

Let {(X i,Y i), i≥1 } be i.i.d 2 dimensional random vectors with common distribution F(x) . By assuming that F is in the domain of attraction of G and the marginal distribution functions satisfy Von Mises condition, we mainly discuss the locally uniform convergence related to density of { M n }, i.e. The paper proves the main results Theorems 1 and 2, which generalize Resnick's result to 2 dimensional case.