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De chi‐kwadraat‐toets voor aanpassing van continue verdelingen
Author(s) -
Hermans J.
Publication year - 1969
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1969.tb00098.x
Subject(s) - mathematics , null distribution , asymptotic distribution , goodness of fit , chi square test , distribution (mathematics) , test statistic , combinatorics , kolmogorov–smirnov test , statistics , statistic , f distribution , class (philosophy)
Summary A description is given of the version of the chi‐square test of goodness‐of‐fit proposed by G. S. W atson (1957, 1958). This version is applicable if one has a full sample x 1 , x 2 ,… xn from a (under the null‐hypothesis) continuous distribution. To estimate the unknown parameters it uses (as will be general practice in this situation) the sample values x and not the class‐numbers n 1 , n 2 ,…, n k . To calculate the asymptotic distribution of the test statistic a more detailed description is given of a method originally proposed by H arper and M ac D onald (1960). Some numerical calculations in case of the normal distribution lead to the conclusion that the asymptotic distribution may be well approximated by a x 2 distribution.