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The Nontruncated Marginal of a Truncated Bivariate Normal Distribution

Published online by Cambridge University Press:  01 January 2025

Barry C. Arnold ,
Robert J. Beaver ,
Richard A. Groeneveld  and
William Q. Meeker
Barry C. Arnold
Affiliation:
Department of statistics, University of California, Riverside
Robert J. Beaver
Affiliation:
Department of statistics, University of California, Riverside
Richard A. Groeneveld*
Affiliation:
Department of Statistics, Iowa State University
William Q. Meeker
Affiliation:
Department of Statistics, Iowa State University
*
Requests for reprints should be sent to Richard A. Groeneveld, Department of Statistics, Iowa State University, Ames, IA 50011.
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Abstract

Inference is considered for the marginal distribution of X, when (X, Y) has a truncated bivariate normal distribution. The Y variable is truncated, but only the X 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 large n. 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.

Keywords

monitored variableprofile likelihoodscreeningskew-normal distribution
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 3 , September 1993 , pp. 471 - 488
Copyright
Copyright © 1993 The Psychometric Society

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