Example of output graph
|Developer(s)||Institute for Land Reclamation and Improvement (ILRI)|
|Operating system||Microsoft Windows|
Originally the method was developed for the analysis of hydrological measurements of spatially varying magnitudes (e.g. hydraulic conductivity of the soil) and of magnitudes varying in time (e.g. rainfall, river discharge) to find their return periods. However, it can be used for many other types of phenomena, including those that contain negative values.
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. The following probability distributions are included: normal, lognormal, logistic, loglogistic, exponential, Cauchy, Fréchet, Gumbel, Pareto, Weibull, Generalized extreme value distribution, Laplace distribution, Burr distribution (Dagum mirrored), Dagum distribution (Burr mirrored), Gompertz distribution, Student distribution and other.
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. The ranges are separated by a break-point. The use of such composite (discontinuous) probability distributions can be useful when the data of the phenomenon studied were obtained under different conditions.
Further it gives the option to see the Q–Q plot in terms of calculated and observed cumulative frequencies.
Generalization of symmetrical distributions (like the normal and the logistic) makes them applicable to data obeying a distribution that is skewed to the right (using an exponent <1) as well as to data obeying a distribution that is skewed to the left (using an exponent >1). This enhances the versatility of symmetrical distributions.
Skew distributions can be mirrored by distribution inversion (see survival function, or complementary distribution function) to change the skewness from positive to negative and vice versa. This amplifies the number of applicable distributions and increases the chance of finding a better fit. CumFreq makes use of that opportunity.
When negative data are present that are not supported by a probability distribution, the model performs a distribution shift to the positive side while, after fitting, the distribution is shifted back.
The figure to the right shows the variation that may occur when obtaining samples of a variate that follows a certain probability distribution. The data were provided by Benson.
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.
Also, it clarifies that the experimentally found best fitting probability distribution may deviate from the true distribution.
Goodness of fit
Cumfreq produces a list of distributions ranked by goodness of fit.
Histogram and density function
The software offers the option to use a probability distribution calculator. The cumulative frequency and the return period are give as a function of data value as input. In addition, the confidence intervals are shown. Reversely, the value is presented upon giving the cumulative frequency or the return period.
- Independent online review of CumFreq: https://www.predictiveanalyticstoday.com/cumfreq/
- Frequency and Regression Analysis. Chapter 6 in: H.P.Ritzema (ed., 1994), Drainage Principles and Applications, Publ. 16, pp. 175–224, International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. ISBN 90-70754-33-9 . Free download as PDF from : ILRI website or from : 
- Intro to composite probability distributions
- Drainage research in farmers' fields: analysis of data, 2002. Contribution to the project “Liquid Gold” of the International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. 
- Benson, M.A. 1960. Characteristics of frequency curves based on a theoretical 1000 year record. In: T.Dalrymple (ed.), Flood frequency analysis. U.S. Geological Survey Water Supply paper 1543−A, pp. 51–71
- Software for probability distribution fitting