On extremal indices greater than one for a scheme of series

The classic extremal index θ is an important parameter of asymptotic behavior of maxima of stationary random sequences. For applications, however, it is interesting to investigatemore complex structures. Recently, the extremal index was generalized to a scheme of series of random length. If the exact extremal index does not exist, then we consider partial indices. In contrast to the classic index, partial indices can be greater than one. In this paper, we consider a new model, where left and right partial indices can be greater than one and equal to each other, although the exact index does not exist.