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CumFreq uses the plotting position approach to estimate the cumulative frequency of each of the observed magnitudes in a data series of the variable. [2] The computer program allows determination of the best fitting probability distribution. Alternatively it provides the user with the option to select the probability distribution to be fitted.
Cumulative frequency distribution, adapted cumulative probability distribution, and confidence intervals. Cumulative frequency analysis is the analysis of the frequency of occurrence of values of a phenomenon less than a reference value. The phenomenon may be time- or space-dependent. Cumulative frequency is also called frequency of non-exceedance.
The image on the right, made with CumFreq, illustrates an example of fitting the log-normal distribution to ranked annually maximum one-day rainfalls showing also the 90% confidence belt based on the binomial distribution. [79] The rainfall data are represented by plotting positions as part of a cumulative frequency analysis.
The cumulative frequency is the total of the absolute frequencies of all events at or below a certain point in an ordered list of events. [ 1 ] : 17–19 The relative frequency (or empirical probability ) of an event is the absolute frequency normalized by the total number of events:
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.
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 ...
The blue picture, made with CumFreq, illustrates an example of fitting the Fréchet distribution to ranked annually maximum one-day rainfalls in Oman showing also the 90% confidence belt based on the binomial distribution. The cumulative frequencies of the rainfall data are represented by plotting positions as part of the cumulative frequency ...
The blue picture illustrates an example of fitting the logistic distribution to ranked October rainfalls—that are almost normally distributed—and it shows the 90% confidence belt based on the binomial distribution. The rainfall data are represented by plotting positions as part of the cumulative frequency analysis.