In many applications it is important to evaluate the impact of clusters of observations caused by the dependence and heaviness of tails of time series. We consider a stationary sequence of random variables (rvs) fRngn1 with marginal cumulative distribution function F(x) and the extremal index  2 [0; 1]. The clusters contain consecutive exceedances of the time series over a threshold u separated by return intervals with consecutive non-exceedances.