| Abstract [eng] |
Asymptotic analysis of maxima of two-dimensional vectors is presented in this paper. It is very important to estimate convergence rate of approximation maxima distribution with limiting distribution function. Transfer theorem for vectors is used. Limiting distribution are also obtained. We showed, that estimation of convergence rate of linearly normalized maxima can be adjusted for maxima of vectors. Besides, it is proved for nonlinearly normalized maxima. Result extends univariate results of A. Aksomaitis. We normalized maxima linearly (Pareto and logistic distributions) and nonlinearly (log-Pareto distribution) to find limiting distribution functions. These functions are more various then three classic in scheme of univariate maxima. Estimations of convergence rate are obtained for each of functions. Queue of convergence rate is 1/n aspect n for Pareto, logistic and log-Pareto distributions and it do not depend on internecine dependence of components. Though, limiting distribution function for log-Pareto distribution is different when components are dependent, while it is the same for logistic and Pareto distributions. Estimation of convergence rate for log-Pareto distribution is more complicated. |
