Bivariate Distributions Compatible or Nearly Compatible with Given Con di tion

ABSTRACT Let ( X , Y ) denote a two dimensional discrete random variable. Assume that exact or approximate statements are provided with regard to the conditional distributions of X given Y and of Y given X . This list of statements may be incompatible in the sense that no joint distribution for ( X . Y ) will satisfv all the statements in the list. Measurement of the degree of incompatibility and identification of most nearly compatible distributions is discussed in the present paper.