Example
We could test the hypothesis that computers fail more during some times of the year than others. To test this, we would collect the dates on which the test set of computers had failed and build an empirical distribution function. The null hypothesis is that the failures are uniformly distributed. Kuiper's statistic does not change if we change the beginning of the year and does not require that we bin failures into months or the like. Another test statistic having this property is the Watson statistic, which is related to the Cramér–von Mises test.
However, if failures occur mostly on weekends, many uniform-distribution tests such as K-S would miss this, since weekends are spread throughout the year. This inability to distinguish distributions with a comb-like shape from continuous distributions is a key problem with all statistics based on a variant of the K-S test. Kuiper's test, applied to the event times modulo one week, is able to detect such a pattern.
Read more about this topic: Kuiper's Test
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)