## Abstract

Consider a two-dimensional discrete random variable (X, Y ) with possible values 1, 2, . . . , I for X and 1, 2, . . . , 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) divergence and power divergence statistics 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 statistics for some illustrative examples.

Original language | English |
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Pages (from-to) | 178-204 |

Number of pages | 27 |

Journal | Studia Scientiarum Mathematicarum Hungarica |

Volume | 54 |

Issue number | 2 |

Early online date | 19 Aug 2017 |

DOIs | |

Publication status | Published - 2017 |

## Keywords

- Conditional specification
- Divergence measures
- Incompatible conditionals
- Iterative algorithm
- Linear programming