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Thus, the mean time between peaks, including the residence time or mean time before the very first peak, is the inverse of the frequency of exceedance N −1 (y max). If the number of peaks exceeding y max grows as a Poisson process, then the probability that at time t there has not yet been any peak exceeding y max is e −N(y max)t. [6] Its ...
The theoretical return period between occurrences is the inverse of the average frequency of occurrence. For example, a 10-year flood has a 1/10 = 0.1 or 10% chance of being exceeded in any one year and a 50-year flood has a 0.02 or 2% chance of being exceeded in any one year.
An estimate of the uncertainty in the first and second case can be obtained with the binomial probability distribution using for example the probability of exceedance Pe (i.e. the chance that the event X is larger than a reference value Xr of X) and the probability of non-exceedance Pn (i.e. the chance that the event X is smaller than or equal ...
Gumbel has also shown that the estimator r ⁄ (n+1) for the probability of an event — where r is the rank number of the observed value in the data series and n is the total number of observations — is an unbiased estimator of the cumulative probability around the mode of the distribution.
Cumulative frequency is also called frequency of non-exceedance. Cumulative frequency analysis is performed to obtain insight into how often a certain phenomenon (feature) is below a certain value. This may help in describing or explaining a situation in which the phenomenon is involved, or in planning interventions, for example in flood ...
Buffered probability of exceedance (bPOE) is a function of a random variable used in statistics and risk management, including financial risk. The bPOE is the probability of a tail with known mean value . The figure shows the bPOE at threshold (marked in red) as the blue shaded area.
Probability of precipitation (PoP) is a commonly used term referring to the likelihood of precipitation falling in a particular area over a defined period of time, which is commonly a day, half day, or hour. The PoP measure is meaningless unless it is associated with an interval of time.
Assuming no systematic errors, the probability the system survives during a duration, T, is calculated as exp^(-T/MTBF). Hence the probability a system fails during a duration T, is given by 1 - exp^(-T/MTBF). MTBF value prediction is an important element in the development of products.