8.4.4.1 Weighted Anderson–Darling Goodness-of-Fit Tests for Heavy Tails

In the case of the AD form of the CvM test statistic Q, the test is performed according to the following stages in Algorithm 8.3. As it turns out two of the more important results one can derive for the asymptotic expansions of the right tail of the AD test statistic, under the nominal claim, are based on a result derived by Zolotarev (1961); we provide this result in Theorem 8.8.

In Figure 8.7, the distribution for the random sum

(8.81)images

is displayed as a function of sample size n with two different weight functions for images given by the following:

  • Case 1: weight ...

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