Summary: The CumFreq 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), and Gumbel probability distributions, and
selects the best fitting 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
Cumfreq 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 software.
Further, Cumfreq uses mirrored distributions that
reverse the skewness, so that the number of
distributions that are possibly applicable is
Cumfreq 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 CumFreq is totally free. It
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
The resulting probability distribution is
accompanied by 90% confidence limits and belts
(bands) and return periods (recurrence
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.
Examples are given.
The program starts clicking on CumFreq.Exe.
More details are given in the program itself.
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
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
reports & cases
reports & cases