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1 results

  • The Nontruncated Marginal of a Truncated Bivariate Normal Distribution

  • Barry C. Arnold, Robert J. Beaver, Richard A. Groeneveld, William Q. Meeker
  • Journal:
    Psychometrika / Volume 58 / Issue 3 / September 1993
    Published online by Cambridge University Press:
    01 January 2025, pp. 471-488

  • 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.