Uji Kuiper

Dina statistik, uji Kuiper raket jeung uji Kolmogorov-Smirnov nu geus leuwih ilahar dipaké (atawa leuwih ilahar disebut uji K-S). Sakumaha uji K-S, kuantitas D+ jeung D- diitung nu nunjukkeun simpangan maksimum saluhureun jeung sahandapeun dua sebaran kumulatif nu keur dibandingkeun. Trik dina tes Kuiper dipaké keur ngitung D+ + D- minangka tes statistik. Parobahan nu leutik ieu maké tes Kuiper minangka sensitip dina buntut minangka median sarta maké invarian ieu dina transformasi nu méter tina variable mandiri. Uji Anderson-Darling mangrupa uji séjén nu nyadiakeun sénsitivitas nu sawanda na buntut (Ing. tail) minangka médian, tapi teu nyadiakeun invarians siklik.

This invariance makes Kuiper's test invaluable when testing for variations by time of yéar or day of the week or time of day.  One example would be to test the hypothesis that computers fail more in some parts of the yéar than others.  To test this, we would collect the dates on which the test set of computers had failed and build a cumulative distribution.  The null hypothesis is that the failures are uniformly distributed.  Kuiper's statistic does not change if we change the beginning of the yéar and doesn't require that we bin failures into months or anything like that.

A test like this would, however, tend to miss the fact that failures occur only on weekends since weekends are spréad throughtout the yéar.  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.

Statistika