Distribution Analyzer



Tool for executing variables sampling plans.  State of the art procedures for testing for normality and transforming nonnormal data.  Makes confidence statements as to the percent conforming to specifications.



Version 1.2 for Windows XP, Vista, 7, 8, 10 and 11, including 64-bit versions.

Download Full Version of Software Above – Try it Free for 30 Days

A full version of the software can be downloaded above and used for free for a 30-day trial.  After 30 days, if you want to continue using the software, you must purchase a license.  The file da12.exe will be downloaded.  Executing this file will install the software on your system including the user’s guide.

Purchasing Software

To continue using the software after the 30-day trial period, you must purchase a license for the software.  A user name and license code will be emailed to you along with further instructions.   You also get free upgrades for 1 year.  Site licenses are also available.

Distribution Analyzer Site Licenses


Distribution Analyzer is a shareware software package for identifying a distribution that best fits a set of data and for estimating expected ranges for future values.  It provides a means of performing Normal Tolerance Intervals (K-intervals) and Variables Sampling Plans on data that does not fit the normal distribution.  The analysis performed includes:

  • Selection of Best Fit Distribution and Estimation of Parameters
  • Test of Whether Selected Distribution Adequately Fits the Data
  • Determination of a Transformation (Function) That Can be Applied to Data so that Transformed Data Fits the Normal Distribution
  • Construction of Tolerance Intervals  Including a Specified Percentage of the Future Values (Normal Tolerance Interval)
  • Confidence Statements for Percentage of Future Values in Spec (Variables Sampling Plan)

Take an example of break force values shown below.  There is a lower spec limit of 4 pounds:

An initial analysis of the data is shown below.  By default, the normal distribution is assumed.  The best fit normal distribution is shown in blue along with a histogram of the data.  The Test of Fit indicates the normal distribution does not adequately fit this set of data.

Clicking the Find Best Distribution button identifies the Largest Extreme Value family of distributions as the best fit.  The analysis for this distribution is shown below.  The Test of Fit passes, so the Largest Extreme Value Distribution adequately fits the fit and can be used as the basis for further analysis.

Having passed the Test of Fit, ranges for future values are provided.  First is the Tolerance Interval:

“With 95% confidence, more than 99% of the values are above 5.07.”

This is akin to the Normal Tolerance Interval or K-Interval but does not assume normality.

The second is relative to the spec limits:

“With 95% confidence, less than 0.0031% of the values are out of spec.”

This is akin to a variables sampling plan but does not assume normality.


  • Can quickly find the distribution that best fits the data
  • Includes the following basic distributions:
    • Beta distribution
    • Exponential and Negative Exponential distributions
    • Largest Extreme Value family:
      • Fréchet distribution
      • Largest Extreme Value distribution
      • Negative Weibull distribution
    • Smallest Extreme Value family:
      • Weibull distribution
      • Smallest Extreme Value distribution
      • Negative Fréchet distribution
    • Gamma and Negative Gamma distributions
    • Johnson Family of Distributions
    • Logistic family
      • Logistic distribution
      • Loglogistic and Negative Loglogistic distributions
    • Lognormal and Negative Lognormal distributions
    • Normal distribution
    • Pearson Family of Distributions
    • Uniform distribution
  • The above distributions include, as special cases, Chi-Square, Erlangian, Fisk, Log Exponential.
  • In addition, log-distributions are included for all the above distributions (log-Beta, log-Weibull, …)
  • Fit Distributions Using Methods of Moments and Maximum Likelihood (using restrictions that ensure data and spec limits are within the range of bounded distributions).
  • Test whether distribution adequately fits the data
  • Generate a tolerance interval for future values and confidence interval for the percentage of future values in spec.
  • Generate random values for all the above distributions
  • Display Skewness-Kurtosis plots to understand relationships between distributions
  • Calculate probabilities and percentiles of the above distributions


  • Simple to use.  Novice users can just enter the data and click on at most 3 buttons.  You don’t have to be familiar with all the distributions.
  • You don’t have to know Greek.  All distributions are represented by their moments (average, standard deviation, skewness, …).  It is easy to compare distributions and generate random numbers from different distributions with the same mean, standard deviation, skewness, etc.
  • Complete control.  Advanced users can specify distributions to use, specify bounds and parameters of the distribution.  You can see the parameters of the distribution as moments or in Greek form.
  • Capabilities not found anywhere else
    • Confidence statements relative to the percent in spec
    • A wider range of distributions than any other package
    • Handles bounded distributions and bounds on data to ensure meaningful results  (the spec limits are always within the range of the distribution).

Further Information

Other Information on Executing Variables Sampling Plans, Testing for Normality and Transforming Nonnormal Data

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