The nontruncated marginal of a truncated bivariate normal distribution |
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Authors: | Barry C. Arnold Robert J. Beaver Richard A. Groeneveld William Q. Meeker |
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Affiliation: | (1) Department of statistics, University of California, Riverside;(2) Department of Statistics, Iowa State University, 50011 Ames, IA |
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Abstract: | Inference is considered for the marginal distribution ofX, when (X, Y) has a truncated bivariate normal distribution. TheY variable is truncated, but only theX values are observed. The relationship of this distribution to Azzalini's skew-normal distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini distribution. Samples that are uniformative about the skewness of this distribution may occur, even for largen. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model. |
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Keywords: | monitored variable profile likelihood screening skew-normal distribution |
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