TEST CRITERIA FOR PEARSON TYPE III DISTRIBUTIONS.
Final rept., Feb 62-Jan 63,
C-E-I-R INC BEVERLY HILLS CALIF
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Goodness-of-fit tests for the family of Pearson Type III distributions, and certain subfamilies, are investigated. A generally applicable com puter program to calculate the large-sample distribution of the parametric Cramer-von Mises statistic, W sub n squared of theta equals M times the integral the square of the differ ence of F sub n of X and F of X theta d F X theta, for an efficient estimator is de veloped and applied to the Pearson Type III dis tribution, the gamma distribution, and the exponential distribution. The large-sample dis tribution theory of W sub n squared of theta is extended, and theoretical results on additional goodness-of-fit tests are derived. Results of sampling experiments are presented to indicate the appropriateness of the tabulated large sample results to samples of moderate size, and sensitivity to the particular form of the esti mators used. Results of sampling experiments are presented to indicate the low efficiency of the Pearson criterion K for testing whether a sample has been drawn from a Pearson Type III distribution. Author