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Distribution Fitting

Find which distribution your data follow: all 8 candidates are fitted, the one with the lowest AIC is chosen, and its probability density is overlaid on the histogram. Useful before nonnormal capability or reliability analysis.

1Data Table

Paste a table copied from Excel into a cell (Ctrl+V). Click a column header (A, B…) before pasting to use the first line as column names. Double-click a header to rename it, right-click to insert/delete rows and columns, and formulas such as =A1*2 work too.

2Distribution Fit Options

Select the columns to fit distributions to (multiple allowed):

How to fit distributions

  1. Copy the measurement column to examine together with its header.
  2. Click the column header (A) in the data table and paste - the first line becomes the column name. You can also open a CSV or Excel file.
  3. Select the columns to fit (each column gets its own result).
  4. Press Analyze and check the best distribution, the AIC ranking (top 5) and the parameter values.

Candidates and fitting method

Normal, lognormal, Weibull, exponential, gamma, logistic, smallest extreme value and largest extreme value are fitted by maximum likelihood (MLE). Lognormal, Weibull and gamma are 3-parameter forms with a location (threshold) parameter (exponential has 2), computed the same way as SciPy, which the Qstat desktop program uses.

Choosing by AIC

AIC = 2×(number of parameters) - 2×(log-likelihood); it is smaller for distributions that describe the data well with fewer parameters. The distribution with the lowest AIC is chosen; fewer than 8 valid values are not fitted.

How to read the distribution fit

  • Distributions whose AIC differs by less than about 2 fit practically equally well - check the top-5 ranking.
  • Also check visually that the curve follows the peak and tails of the histogram.
  • Use the result to choose the distribution for nonnormal capability or reliability (life data) analysis.

Frequently asked questions

What is the order of the parameters?

The same as SciPy: (shape, location, scale) for distributions with a shape parameter, otherwise (location, scale).

How many values do I need?

At least 8; 30 or more are recommended to judge the distribution.

Is there a goodness-of-fit p-value?

This feature compares candidates by AIC. Check normality with a p-value on the normality test page.

Is my data sent to a server?

No. All calculations run inside your browser and nothing is transmitted or stored.

Other chart tools

Normality Test (Anderson-Darling)Test for normality with the Anderson-Darling A², p-value and a histogram.Histogram MakerSee the distribution, a fitted normal curve and Pp/Ppk against spec limits at once.Normal Probability Plot (QQ Plot) MakerCheck whether data follow a normal distribution with a QQ plot and R².

Need process capability, control charts or DOE?

The Qstat desktop program offers about 250 analysis features: histograms and box plots plus process capability (Cp, Cpk), control charts, measurement system analysis (MSA), design of experiments (DOE), regression and machine learning.

Try Qstat free for 30 days