yielded by this formula hold approximately. If in such a way that then Take where T is return interval n is number of years on record; m is the number of recorded occurrences of the event being considered Example Given that the return period of an event is 100 years, So the probability that such an event occurs exactly once in 10 successive years is: Risk analysis Return period is useful for risk analysis (such as natural, inherent, or hydrologic risk of failure). When dealing with structure design expectations, the return period is useful in calculating the riskiness of the structure. The probability of at least one event that exceeds design limits during the expected life of the structure is the complement of the probability that no events occur which exceed design limits. The equation for assessing this parameter is where is the expression for the probability of the occurrence of the event in question in a year; n is the expected life of the structure. See also 100-year flood Cumulative frequency analysis Frequency of exceedance Residence time References Hydrology Seismology Time in science