日本統計学会誌
Online ISSN : 2189-1478
Print ISSN : 0389-5602
ISSN-L : 0389-5602
LIMITING MOMENT GENERATING FUNCTION OF CRAMÉR-VON MISES-SMIRNOV GOODNESS OF FIT STATISTICS UNDER NULL LOCAL ALTERNATIVES
Seiji Nabeya
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ジャーナル フリー

1992 年 22 巻 2 号 p. 113-122

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In this paper the limiting distribution of Carmér-von Mises-Smirnov goodness of fit test statistic discussed when the parameters are estimated from the samle. Using the general theory of Durbin (1973 a and b) a method of deriving the limiting moment generating function for the test statistic is proposed under null and under a sequence of local alternatives. Applying this method, the limiting moment generating functions are evaluated for logistic and Cauchy distributions in the case of efficient estimation. Some results of numerical computation are also given.
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© Japan Statistical Society
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