In practical applications it is important to evaluate the impact of clusters of observations caused by the dependencein time series at the estimation of statistical indices. The clusters contain consequent exceedances of time series overa threshold separated by gaps with consequent non-exceedances. We prove asymptotic discrete distributions of the numberof events of interest arising between two clustersof some process over a threshold (random variable 'T') as well as the number of exceedances of the process in the cluster (random variable 'C').
