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SUMMARYThe test statistic X2(1bbl)+X2(b2), where X(1bl) and X(b2) are standardized normal equivalents to the sample skewness, Jbl, and kurtosis, b2, statistics, is considered in normal sampling. Using the Johnson system, Su and SB, as approximate normalizing distributions, contours in the (1bl, b2) plane of the test statistic are set up for sample sizes ranging from 20 to 1000.
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.Approximate formulae for a set of percentage points of the Pearson system are given in terms of the skewness and kurtosis.Some key word8: Fitting by moments; Pearson percentage point; Rational fraction approximation.
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.
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