The Longest Run Statistic Associated With Exchangeable Binary Variables

Abstract

Since the hydrologic risk is defined as a risk of exceedance of a critical level during a period, the number of the longest successive exceedances which is referred to as the longest run statistic shows the length of the longest hydrologic risk period. This paper is concerned with the longest run statistic associated with exceedances. In the derivation of a binary sequence, an independent sequence of random variables and a random threshold are considered. The elements of a binary sequence are assigned with respect to a random threshold. In such a consideration, the elements of the corresponding binary sequence are not independent, but are symmetrically dependent, i.e. exchangeable. The distribution of the longest run statistic is derived for the sequence of exchangeable binary variables and its hydrological use is discussed. © Tübi?tak.