ON THE EFFECT OF TRUNCATION IN SOME OR ALL COORDINATES OF A MULTINORMAL POPULATION
Abstract
A p-dimensional normal random variable X sub-1, X sub-2,..., X sub-p may represent p quantitative traits of an individual; very often an admission test requires that each of these traits be above a certain preassigned value, so that only those individuals pass the test for whom X sub-1 > t sub1,0000, X sub p > t sub-p. Explicit expressions are obtained for the moments E(X sub-i), E(X sub-i squared), E(X sub-i X sub-j), and the procedure for extending the method to the general case of E(X sub-i to the power of m X sub-j to the power of n) is indicated. The possibility of truncation in some but not all coordinates is included since, for example, the case of X sub-1 not truncated, X sub-2 truncated at tau corresponds to t sub-1 = -infinity, t sub-2 = tau. Explicit expressions are also obtained for the marginal probability density function of X sub-1 and for the joint marginal probability density function of (X sub-1, X sub-2), after truncation in X sub1, X sub2,...., X sub-p. Examples are given for the use of some of the results for determining t sub-1, t sub-2,......so that certain preassigned changes in the population are achieved.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 09, 1951
- Accession Number
- AD0007092
Entities
People
- Paul L. Meyer
- Z. W. Birnbaum
Organizations
- University of Washington