Kuiper Q-Q plot

Data input

Paste in values, e.g. 0.3, 1.2, 0.8, 2.5, 0.1, …

Data plotted against reference

If the data mainly lie on the grey diagonal, the data have probably been drawn from the reference distribution. If the data mainly lie off-diagonal, the data are unlikely to have been drawn from the reference distribution. The reference distribution can be selected below.

The vertical lines marked D⁺ and D⁻ indicate the greatest distances above and below the reference distribution, respectively.

Kuiper's statistic

This statistic is based on the D⁺ and D⁻ distances, and gives a precise measurement of how large the deviation from the diagonal is. It is computed using Stephens' modification.

V* =

To determine significance, compare against the following tail probabilities. A sample deviating from the reference is cause for a larger V* than the critical value in the upper tail.

Significance level 10 % 5 % 1 %
Upper tail 1.620 1.747 2.001

If the value of V* is less than that given for the desired significance level in this table, then we cannot rule out the possibility that the sample is drawn from the reference distribution. The reference distribution can be selected below.

Reference distribution

Select the distribution you want to test for membership with. The number underneath the distribution name refers to the AIC score of that distribution. A lower AIC means a better fit for the data.

The MLE button resets custom parameters to the maximum likelihood fit.