|
Download: CumFreq Software & models General articles & manuals Artículos (in Spanish, en Español) Published reports & cases Particular reports & cases FAQ's & answers Update record Home page |
|
Documentation: 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. |
|
Acknowlegments:
Thanks to a suggestion by Madhu Kandampadath the
generalized extreme value (GEV) distribution was
included in the list of options on 17 February
2018. 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. |
|
Hints:
CumFreq can create histograms and
probability density functions as illustrated
on the
density page. An amplified version of CumFreq named CumFreqA can be seen on: composite distributions. This version contains extra facilities regarding composite probability distributions. These are not often found with an exception of the Laplace distribution. The versatility of generalization makes it possible, for example, to fit approximately normally distributed data sets to a large number of different probability distributions, see multple fit, while negatively skewed distributions can be fitted to square normal and mirrored Gumbel distributions, as in left skew, and finally the various possibilities of curved regression are show in curvatures. |
| |
|
Figure 1. Introduction screen to CumFreq program
(model).
The CumFreq calculator models the cumulative (non-exceedance) frequency distribution and fits it to a probability distribution. It uses, amongst other, the normal, logistic, exponential and Gumbel distributions. For distribution fitting, the CumFreq calculator app linearizes the probability distribution.For a list of linearizations, based on logarithmic and other transformations, see: transformations |
| |
|
Figure 2. Input tabsheet
The input tabsheet shows the probability distributions that are being used in the CumFreq calculator model to fit the data to. In this application program one can select "best of all" or indicate a preference. The number of intervals needed to prepare the histogram can be entered, as well as a cut-off (threshold) velue. |
| |
|
Figure 3. Cumulative distribution fitting
Probability distribution fitting is based on plotting positions (the observed data). A 90% confidence interval of the fitted probability distribution is shown. It is a specialty of the CumFreq calculator model calculator to apply "generalized" distributions, which, in this application program, makes them fit better than the standard ones. They are based on an exponential transformation of the data to obtain a closer fit. The curve shown is also called cumulative distribution function (PDF). |
| |
|
Figure 4. Histogram of fitted distribution + density
function
The histogram provides the observed and calculated frequencies by interval. The histogram gives an impression of the symmetry of the probability distribution and whether it is skew to the left or to the right. The probability density function (PDF) is shown as the product of density and lenhth of the intervals. |
| |
|
Figure 5. Probability distributions ranked by goodness
of fit
CumFreq provides the option to produce a list of probability distributions ranked by goodness of fit. |
| |
|
Figure 5. Calculator
CumFreq provides the option to calculate probabilities of data values and vice versa. The same holds for return periods. In addition confidence intervals are given. |
| |
|
Figure 6. Composite probabilty distributions.
The amplified CumFreq calculator (CumFreqA) provides the possibility to select a composite probability distribution (like the Laplace distribution) or to find the best fitting of all. See: composite distribution. |
| |
|
Figure 7. Bimodal probabilty distribution.
The amplified CumFreq calculator (CumFreqA) in some cases comes up with a bimodal probability disribution. See also: bimodal distribution. |