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Symmetry test

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A statistical test for testing the hypothesis that a one-dimensional probability density is symmetric about zero.

Let the hypothesis of symmetry be that the probability density of the probability law of independent random variables is symmetric about zero, that is, for any from the domain of definition of . Any statistical test intended for testing is called a symmetry test.

Most often the hypothesis that all the random variables have probability density , , is considered as the alternative to . In other words, according to the probability density of is obtained by shifting the density along the -axis by a distance , to the right or left according to the sign of . If the sign of the displacement is known, then is called one-sided, otherwise it is called two-sided. A simple example of a symmetry test is given by the sign test.

Usually a randomization test is used for testing symmetry.

References

[1] Z. Sidak, "Theory of rank tests" , Acad. Press (1967)
[2] M.G. Kendall, A. Stuart, "The advanced theory of statistics" , 2. Inference and relationship , Griffin (1979)
How to Cite This Entry:
Symmetry test. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Symmetry_test&oldid=31876
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article