Anderson–Darling Test

Reference work entry
DOI: https://doi.org/10.1007/978-0-387-32833-1_11
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The Anderson–Darling test is a goodness-of-fit test which allows to control the hypothesis that the distribution of a random variable observed in a sample follows a certain theoretical distribution. In particular, it allows us to test whether the empirical distribution obtained corresponds to a normal distribution.

HISTORY

Anderson, Theodore W. and Darling D.A. initially used Anderson–Darling statistics, denoted A2, to test the conformity of a distribution with perfectly specified parameters (1952 and 1954). Later on, in the 1960s and especially the 1970s, some other authors (mostly Stephens) adapted the test to a wider range of distributions where some of the parameters may not be known.

MATHEMATICAL ASPECTS

Let us consider the random variableX, which follows the normal distribution with an expectation μ and a variance \( { \sigma^2 } \)

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REFERENCES

  1. 1.
    Anderson, T.W., Darling, D.A.: Asymptotic theory of certain goodness of fit criteria based on stochastic processes. Ann. Math. Stat. 23, 193–212 (1952)CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Anderson, T.W., Darling, D.A.: A test of goodness of fit. J. Am. Stat. Assoc. 49, 765–769 (1954)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Durbin, J., Knott, M., Taylor, C.C.: Components of Cramer-Von Mises statistics, II. J. Roy. Stat. Soc. Ser. B 37, 216–237 (1975)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Stephens, M.A.: EDF statistics for goodness of fit and some comparisons. J. Am. Stat. Assoc. 69, 730–737 (1974)CrossRefGoogle Scholar

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