The nontruncated marginal of a truncated bivariate normal distribution


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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Correspondence to Richard A. Groeneveld.

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Arnold, B.C., Beaver, R.J., Groeneveld, R.A. et al. The nontruncated marginal of a truncated bivariate normal distribution. Psychometrika 58, 471–488 (1993).

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Key words

  • monitored variable
  • profile likelihood
  • screening
  • skew-normal distribution