CumFreq

CumFreq uses the plotting position approach to estimate the cumulative frequency of each of the observed magnitudes in a data series of the variable.

Another characteristic of CumFreq is that it provides the option to use two different probability distributions, one for the lower data range, and one for the higher.

[3] During the input phase, the user can select the number of intervals needed to determine the histogram.

ILRI[5] provides examples of application to magnitudes like crop yield, watertable depth, soil salinity, hydraulic conductivity, rainfall, and river discharge.

The program can produce generalizations of the normal, logistic, and other distributions by transforming the data using an exponent that is optimized to obtain the best fit.

This feature is not common in other distribution-fitting software which normally include only a logarithmic transformation of data obtaining distributions like the lognormal and loglogistic.

[6] The confidence belt around an experimental cumulative frequency or return period curve gives an impression of the region in which the true distribution may be found.

Screenprint of input tabsheet
Composite (discontinuous) distribution with confidence belt [ 4 ]
(A) Gumbel probability distribution skew to right and (B) Gumbel mirrored skew to left
Nine return period curves of 50-year samples from a theoretical 1000-year record (base line)
List of probability distributions ranked by goodness of fit, example
Histogram and probability density of a data set fitting the GEV distribution [ 7 ]
Probability distribution calculator as used in the CumFreq software