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 A 2, 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 variable X, which follows the normal distribution with an expectation μ and a variance \( { \sigma^2 } \), and has a distribution function \( { F_X (x; \theta) } \), where θ is a parameter (or a set of parameters) that determine, F X . We furthermore...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
REFERENCES
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)
Anderson, T.W., Darling, D.A.: A test of goodness of fit. J. Am. Stat. Assoc. 49, 765–769 (1954)
Durbin, J., Knott, M., Taylor, C.C.: Components of Cramer-Von Mises statistics, II. J. Roy. Stat. Soc. Ser. B 37, 216–237 (1975)
Stephens, M.A.: EDF statistics for goodness of fit and some comparisons. J. Am. Stat. Assoc. 69, 730–737 (1974)
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
(2008). Anderson–Darling Test. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_11
Download citation
DOI: https://doi.org/10.1007/978-0-387-32833-1_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-31742-7
Online ISBN: 978-0-387-32833-1
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering