Approximation to Percentiles of a Variable of the Bivariate Normal Distribution When the other Variable is Truncated, with Application

摘要

A Cornish-Fisher expansion is used to approximate the percentiles of a variable of the bivariate normal distribution when the other variable is truncated. The expression is in terms of the bivariate cumulants of a singly truncated bivariate normal distribution. The percentiles are useful in the problem of personnel selection where we use a screening variable to screen applicants for employment and a correlated performance variable to screen employees for rehiring. This paper provides a bivariate cumulants table for determining the cutoff score of the performance variable. The following two problems are also considered: (1) determine the proportion of applicants who would have been successful had no screening been applied, and (2) determine the proportion of individuals being rejected by screening who would have been successful had they been hired. The variable that is used to measure job performance and the variable that measures the outcome of an aptitude test are assumed to be jointly distributed with correlation p. This is a reprint from connections is statistics.