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  2. Frequency of exceedance - Wikipedia

    en.wikipedia.org/wiki/Frequency_of_exceedance

    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 ...

  3. Buffered probability of exceedance - Wikipedia

    en.wikipedia.org/wiki/Buffered_probability_of...

    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.

  4. Confidence and prediction bands - Wikipedia

    en.wikipedia.org/wiki/Confidence_and_prediction...

    Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.

  5. Probability distribution fitting - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution...

    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 ...

  6. Gumbel distribution - Wikipedia

    en.wikipedia.org/wiki/Gumbel_distribution

    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.

  7. Cumulative frequency analysis - Wikipedia

    en.wikipedia.org/wiki/Cumulative_frequency_analysis

    Histogram derived from the adapted cumulative probability distribution Histogram and probability density function, derived from the cumulative probability distribution, for a logistic distribution. The observed data can be arranged in classes or groups with serial number k. Each group has a lower limit (L k) and an upper limit (U k).

  8. Probability of precipitation - Wikipedia

    en.wikipedia.org/wiki/Probability_of_precipitation

    The hourly PoP is the probability that more than 0.01 inches (0.25 mm) of precipitation would occur if conditions like those in the given hour continued for twelve hours. It can be similar to the daily PoP and vary little, or it can vary dramatically. the daily PoP will be the average of the hourly PoP across the whole day.

  9. Generalized extreme value distribution - Wikipedia

    en.wikipedia.org/wiki/Generalized_extreme_value...

    In probability theory and statistics, the generalized extreme value (GEV) distribution [2] is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions.

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