Abstract
Some power series approximations to the exact null distribution of the chi-bar-square statistic for several testing situations are developed using the first four cumulants of the null distributions, and their performance is investigated numerically. The series expansions use Laguerre polynomials and the associated gamma densities. Chi-bar-square statistics arise when testing the homogeneity of normal means with the alternative restricted by a partial ordering against all alternatives. Approximations are provided for the case of a total order and a simple tree with equal, or nearly equal, sample sizes. The numerical investigations indicate the accuracy and usefulness of these approximations.
This research was partially sponsored by the Office of Naval Research under ONR contract N00014-80-C0322.
AMS 1980 subject classifications; Primary 62F03; Secondary 62E20.
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© 1986 Springer-Verlag Berlin Heidelberg
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Singh, B., Wright, F.T. (1986). Power Series Approximations to the Null Distributions of Some Chi-Bar-Square Statistics. In: Dykstra, R., Robertson, T., Wright, F.T. (eds) Advances in Order Restricted Statistical Inference. Lecture Notes in Statistics, vol 37. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9940-7_14
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DOI: https://doi.org/10.1007/978-1-4613-9940-7_14
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