Individual Distribution Identification: Automatically Find the Best-Fitting Distribution
What is Individual Distribution Identification?
Individual distribution identification fits several candidate distributions to the same data, including normal, lognormal, 3-parameter Weibull, exponential, Gamma and logistic, and evaluates goodness of fit with Anderson-Darling statistics or correlation coefficients. The candidates are ranked by fit and each gets a probability plot, helping you determine the most plausible distribution so downstream analyses use the right method. Fitting many distributions in parallel avoids settling on one or two candidates and missing a better model.
When to Use It
Use it when you do not know what distribution the data follow: choosing a distribution before non-normal capability analysis, reliability and life data analysis, distribution assumptions for simulation, and diagnosing skewed data. The identified distribution can feed the quantile calculation of a non-normal CpK tool or a reliability analysis. It is the standard first step when data normality is in doubt.
How to Use It (Step by Step)
Paste the data and the tool fits the candidate distributions, ranks them by Anderson-Darling value and draws the probability plots. Compare the AD values, where smaller is better, and the probability plots, where points closer to the line is better, and choose a distribution that is both a good fit and physically interpretable for the process. Report the chosen distribution and its fit statistics; cross-validate by splitting the sample and refitting if stability matters.
Key Formulas / Example
The Anderson-Darling statistic measures how far the empirical distribution departs from the fitted candidate; it is used for relative comparison rather than an absolute threshold, and the probability plot is more intuitive. For example, life data often fit Weibull or lognormal best, while measurement data from a well-behaved process fit normal. Be cautious with 3-parameter distributions on small samples, where the fit can be unstable.