On the Construction of a Joint Distribution Given Two Discrete Conditionals

• Activity Number: 491
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: International Indian Statistical Association
• Author(s): Indranil Ghosh* and Saralees Nadarajah
• Companies: Austin Peay State University and University of Manchester
• Keywords: Divergence measures ; Epsilon compatibility

Abstract

Consider a two-dimensional discrete random variable $(X,Y)$ with possible values $1,2,\ldots, I$ for $X$ and $1,2,\ldots, J$ for $Y$. For specifying the distribution of $(X,Y)$, suppose both conditional distributions of $X$ given $Y$ and $Y$ given $X$ are specified. In this paper, we address the problem of determining whether a given set of constraints involving marginal and conditional probabilities and expectations of functions are compatible or most nearly compatible. To this end, we incorporate all those information with the Kullback-Leibler (K-L) divergenceand power divergence measures to obtain the most nearly compatible probability distribution when the two conditionals are not compatible, under the discrete set up.Finally, a comparative study is carried out between the K-L divergence and power divergence measures for some illustrative examples.