CumFreq, distribution fitting of probability, free calculator
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Summary: The CumFreq model program calculates
the
cumulative (no exceedance, non-exceedance) frequency
and it does probability distribution fitting of data
series, e.g. crop production, soil properties,
salinity, depth to watertable (water-table),
rainfall, river and drain discharge, groundwater
(ground-water) and river level, hydraulic
conductivity and soil permeability for water. The computer program fits various linear, logarithmic, exponential and double exponential cumulative frequency distributions, including the normal, log-normal (lognormal), (log)logistic, Cauchy, Pareto, Weibull, Frechet (Fisher-Tippett type II), Kumaraswamy, Gumbel, GEV, Erlang (Gamma), Burr, Dagum, Laplace, Student, Gompertz, exponential, Poisson and Rayleigh probability distributions, and selects the most appropriate distribution using the method of best fit. Some of the distributions are useful for extreme value analysis. Preference for a specific distribution can also be expressed. The Cumfreq calculator model not only uses logarithmic but also exponential transformations of the data. The exponent (greater than 0) is optimized automatically. These so called generalized distributions have great flexibility, but they are mostly not used in other distribution fitting calculators, except the Burr distribution which is a generalization of Pareto. Further, the Cumfreq application (app) uses mirrored (inverese, complementary) distributions that reverse the skewness, so that the number of distributions that are possibly applicable is enlarged. One of the few existing examples is the inverse (mirrored, complementary) characteristic of the Burr and Dagum distributions. The Cumfreq program calculator allows negative data. In case of distributions that do not support negative data, the distribution is shifted in positive direction so that they are made applicable. The download and use of the CumFreq model program is totally free. It is freeware. |
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Details:
When the mathematical model program detects a
discontnuous probability function, it gives the
user the choice to introduce a breakpoint
(break-point) or threshold value, yielding a
segmented or composite frequency and probability
distribution. The resulting probability distribution is accompanied by 90% confidence limits and belts (bands) and return periods (recurrence intervals). The program also divides the range of data into a number of equal intervals and calculates an interval frequency distribution or histogram. The number of intervals is to be given by the user. On 22 March 2018 the option to see a list of distributions ranked according to their goodness of fit was introduced. On 6 April 2018, next to the cumulative distribution function (CDF), the probability density function (PDF) was inlcluded in the histogram graph. Examples are given. |
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Start: The program starts clicking on CumFreq.Exe. More details are given in the program itself. |
Download:
CumFreq
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A lecture note ("Data Analysis") on statistical analysis with examples of CumFreq applications is found on the articles page. Further, this page gives an article binomial confidence limits for cumulative probability distributions.
The principles of frequency analysis can be found in a lecture note on the FAQ's page. Further, this page gives a summary paper on binomial confidence limits for cumulative frequency distributions.
An article using CumFreqA has appeared in the International Journal of Mathematical Methods, see this site.
An article specialised in application of the generalized logistic distribution can be found as PDF document or on ResearchGate
A paper entitled: "The generalized standard and mirrored Gumbel probability distributions, composite or not, are applicable to many datasets, either symmetrical, skew to the left, or skew to the right" can be read at composite paper or at generalized
A a publication entitled: "How to derive a probability distribution from a data set using the simple method of plotting positions and the free CumFreq model" can be consulted at simple method or at this place
Another publication entitled: "Comparing the results of transmuted Gumbel probability distributions found in literature with those obtained by the free CumFreq program" is to be seen at transmuted Gumbel or at this site
Stil another publication entitled: "Comparing the results of Extended Gumbel Type-2 probability distributions found in literature with those obtained by the free CumFreq program" can be found at extended Gumbel or over here
In case you wish to read: "Comparing the results of Truncated Generalized Frechet Weibull distribution found in literature with those obtained by the free CumFreq program" use the link Frechet Weibull
A list of publications in which CumFreq is used can be seen in this paper
There is an article comparing results of extended probbility distributions found in literature with those obtained using the CumFreqA program that finds best fitting bimodal solutions in: this bimodal article.
Experiences: For improvement, I am interested to learn about your experiences with CumFreq. For this there is a contact form.
Two days later the composite Laplace distribution was added.
On 27 May 2018, thanks to observations of John Haddy, the Burr and Dagum (Burr mirrored) distributions were included. Three days later the Gompertz distribution was incorporated.