The use of nonsystematic flood data for
statistical purposes depends on reliability of assessment both flood magnitudes
and their return period. The earliest known extreme flood year is usually the
beginning of the historical record. Even though the magnitudes of historic
floods are properly assessed, a problem of their retun periods remains
unsolved. Only largest flood (XM) is known during whole historical period and
its occurrence carves the mark of the beginning of the historical period and
defines its length (L). So, it is a common practice of using the earliest known
flood year as the beginning of the record. It means that the L value selected
is an empirical estimate of the lower bound on the effective historical length
M. The estimation of the return period of XM based on its occurrence, i.e. , gives the severe upward bias. Problem is to estimate the
time period (M) representative of the largest observed flood XM. From the discrete
uniform distribution with support of the probability of the L position of XM
one gets
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