Data Analysis & Simulation

Recently a customer has contacted us and noted that the Inverse Cumulative Distribution Function (the Quantile Function) of the Inverse Gaussian distribution implemented in EasyFit works well for lambda=1902.1, mu=41857.0 and P=0.9, but fails for the same lambda & mu and P=0.99. Last week we have released an updated version of EasyFit that fixes the problem, and in this post we would like to elaborate more on the issue.

Evaluating the Inverse CDF of the Inverse Gaussian Model
Since the CDF of the Inverse Gaussian distribution is quite complicated (expressed in terms of the two Laplace Integrals), the Inverse CDF of this model is not available in closed form, and cannot be easily evaluated for a given set of distribution parameters. Initially, we have implemented an iterative approximation algorithm that evaluates the ICDF(P) using the CDF as well as the PDF to speed up the calculation. The algorithm itself works very well over a great range of input parameters, however, we have placed a limitation on how many iterations it is allowed to perform.

Because EasyFit is considered an interactive data analysis tool, we are always looking for a balance between the feature set and the performance, which is especially important when using EasyFit with Excel worksheets calculated in real time. The limitation on the number of iterations is necessary to make sure the algorithm doesn’t fall into an “infinite loop”, meaning the situation when it’s unable to reach the specified accuracy regardless of how long it continues to work. The problem usually happens when we are hitting the precision limitations of the computer’s CPU: in theory, the algorithm must converge in a limited number of steps, but in reality, it will just continue iterating over and over again without any accuracy improvements.

As a solution, we have made some improvements to the algorithm, making it more robust and efficient, so it now works with the same accuracy, but for a larger range of input parameters. For example, considering the parameters that initially caused the problem (lambda=1902.1 and mu=41857.0), the ICDF(P) can be evaluated for values of P up to 0.999925, which is more than enough for most statistical analysis applications.

Should You Upgrade?
Since this minor issue does not affect the accuracy of distribution fitting, you only need to upgrade if you are experiencing problems evaluating the Inverse CDF of the Inverse Gaussian distribution for P>0.9, otherwise EasyFit 5.2 will still work well for you.

We have just released EasyFit Version 5.1 - the update that fixes a bug causing an incorrect calculation of the chi-squared GOF statistic for small sample sizes. To upgrade, uninstall EasyFit 5.0 from your computer, then download and install the latest version.

On April 17 2005, the Millstone nuclear generating plant in Connecticut shut down when a circuit board monitoring a steam pressure line short-circuited. “Tin whiskers” - microscopic growths of the metal from soldering points on a circuit board - were blamed for causing the problem. These whiskers are comprised of nearly pure tin, and are therefore electrically conductive.

Field failures attributable to tin whiskers have cost individual programs many millions of dollars each. As a result, manufacturers of high-reliability systems are forced to use Monte Carlo simulation models to decide whether the use of tin poses an acceptable risk in a given application.

Recently a group of NASA scientists lead by Karim J. Courey, a Principal Engineer with the Orbiter Sustaining Engineering Office, Lyndon B. Johnson Space Center, used our distribution fitting software EasyFit to better understand the underlying process and develop a probability model that can be used to improve existing Monte Carlo risk simulation models… read the full case study

Since fitting probability distributions to large data sets can be a time-consuming task, we are currently researching the possibility of using multi-core processors to make EasyFit work faster. During the past several years, major processor manufacturers have been promoting the multi-core technology on the desktop processors market. Multiple cores in a single chip allow for better performance/price ratio on a range of tasks, however, existing software needs to be updated accordingly to take full advantage of this type of hardware.

We have modified the original distribution fitting algorithm to utilize all cores available on a system, and used it to fit distributions to a simulated set of 200,000 data points. In a series of tests on an Intel dual-core processor, the new algorithm executed almost twice as fast, yielding up to 90% performance increase, compared to the version currently used in EasyFit. These are very good results, and we will definitely be including this feature into the next release of EasyFit.

On a related note, last week we were contacted by a customer regarding our upcoming Simulation & Probabilistic Analysis SDK. They need to analyze large volumes of data, and from their description of the problem we estimated that the typical analysis would take up to 20 hours on a modern PC. With the new distribution fitting algorithm, it can take less than 12 hours on a dual-core CPU, or even less on quad-core processors popular in the server space. In a decision making environment where several hours can mean the difference between profit and loss, this is a very important improvement.

Lately we have received a couple messages from customers asking if it’s possible to use the Monte Carlo simulation and distribution fitting features of EasyFit in their own software applications. The short answer is yes, but these features are limited to calculating some distribution functions in Excel VBA. There’s currently no way to run simulations, fit distributions to data, perform goodness of fit tests, or use distribution functions from C#, C++, VB.NET, and other programming languages.

To fill the gap, we are considering to create a Simulation & Probabilistic Analysis Software Development Kit (SPA SDK) for software developers who need to deal with risk & uncertainty in their applications, but don’t have time or expertise to design and implement the required features on their own. We already have in place the tried and true technology that’s a basis for our distribution fitting products EasyFit and EasyFitXL, so creating an SDK would be possible in a short period of time.

Since we have had only a few requests for an SDK, we would like to know whether you would be interested in such kind of product. Below is our vision for the SDK – you are welcome to express any thoughts or specific requirements you might have. Please feel free to contact us and we will take your input seriously.

Update: The free beta version of the SDK is now available for download - please click here for details.

What is a Simulation & Probabilistic Analysis Software Development Kit (SPA SDK) ? (more…)

EasyFit ships with a comprehensive help file providing detailed information on all aspects of fitting distributions to data and interpreting the analysis results. For instance, it includes the description of supported distributions, goodness of fit tests, and output graphs.

If you are considering to try EasyFit but not sure if it has a particular feature you need, you can refer to the EasyFit help online which we have made available on our website for your convenience. Of course, you are still welcome to contact us for any questions regarding EasyFit or fitting distributions in general.

We are glad to announce that customers from Italy can now purchase EasyFit, our distribution fitting software product, through SxST, the Milan-based company specializing in software solutions for science and technology.

SxST provides a wide range of scientific software products from recognized vendors to Italian businesses, government organizations and academic institutions. According to the agreement, SxST will be offering the Italian version of EasyFit and the first level support in Italian language to their clients, ensuring the best customer experience at the same cost as for the rest of EU countries.

It is really fascinating for us to see EasyFit standing in line with statistical software packages by Systat Software, Minitab, GraphPad, and StataCorp. Our partnership with SxST can be thought of as a milestone indicating that EasyFit has reached the quality level of brand name products offered by these long-established companies.