Power Series Approximations to the Null Distributions of Some Chi-Bar-Square Statistics.
MISSOURI UNIV-ROLLA DEPT OF MATHEMATICS AND STATISTICS
Pagination or Media Count:
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 on the means and when testing the 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. Author
- Statistics and Probability