Notes on the Distribution of √b 1 in Sampling from Pearson Distributions

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYThe distribution of the skewness statistic Vbl in sampling from Pearson Type I distributions is approximated for moderate to large sample sizes and for a limited region of the parameter space. Approximate contours of the power of the Vbl statistic for detecting departures of Pearson Type I distributions from the normal are given. The method uses expansions for the first eight moments along with the Cornish-Fisher expansion for percentiles. For selected parameter points, Monte-Carlo runs were made for comparisons.

Comparison of the alternative parameter estimators of Pearson distributions by robustness criteria

“…The literature about the Pearson distributions can be divided into two groups: while the first group deals with the system itself [4,24,37], the second one reviews some specific distributions in the system [5,7,42].…”

On Testing for the Nullity of Some Skewness Coefficients

“…But this value may become very large, and accordingly, difficult to interpret. However, the classical Ô b ½ -test of skewness is based on this coefficient (see, e.g., Bhattacharya et al, 1982;Mulholland, 1977;Bowman & Shenton, 1973;D'Agostino & Tietjen, 1973;D'Agostino & Pearson, 1973). Each of the other existing measures of skewness (see, e.g., Groeneveld & Meeden, 1984) can provide a natural way to derive a test for skewness.…”

Goodness-of-fit statistics for location-scale distributions

“…An approximation to the distribution of bg was obtained by Anscombe and Glynn (1983). Work on approximating the distribution of /b^ can be found in Bowman andShenton (1973) andD'Agostino andTietjen (1973).…”