Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 1, pp. 23--35

HIDDEN TRUNCATION MODELS

By

BARRY C. ARNOLD and ROBERT J. BEAVER, University of California, Riverside

SUMMARY. Suppose $(\underline{X},Y)$ has a $k+1$ dimensional normal distribution. Consider the conditional distribution of $\underline{X}$ given $Y > y_{0}$, for some fixed value $y_{0} \epsilon {\bf R}$. Such hidden truncation models provide a flexible family of skewed alternatives to the classical $k$ dimensional normal distribution. Distributional properties of these models are investigated. Non-normal variants of the distribution are also discussed as are multiple hidden truncation models. A specific example involving a skewed bivariate data set (heights and weights of athletes) is analysed in detail.

AMS (1991) subject classification. 62H05; 62H12.

Key words and phrases. Skewed-normals, truncated normals, generalized skewed distributions.

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