On a Perturbed Normal Distribution with Application to Analyzing a Screened Data

This paper deals with the screening situation where the samples are drawn from the conditional distribution of a truncated bivariate normal distribution. The initial screening variable is doubly truncated, but only the values of the other variable are observed following the screening. Some properties of this conditional distribution, named as the perturbed normal distribution, are studied. The relationship of the distribution to skew-normal distribution is also obtained. The screened samples that are uninformative about the correlation of the bivariate normal distribution may occur, even for large sample size. MCMC method is employed to eliminate the uncertainty and to estimate the correlation as well as the unscreened population parameters of the conditional distribution. Illustrative examples demonstrate the performance of the method.