THE NONTRUNCATED MARGINAL OF A TRUNCATED BIVARIATE NORMAL-DISTRIBUTION

Inference is considered for the marginal distribution of X, when (X, Y ) has a truncated bivariate normal distribution. The Y variable is tru ncated, but only the X values are observed. The relationship of this d istribution to Azzalini's ''skew-normal'' distribution is obtained. Me thod 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. P rofile likelihood methods are employed to describe the uncertainty inv olved in parameter estimation. A sample of 87 Otis test scores is show n to be well-described by this model.