The thesis presents two methods for analyzing multi-dimensional frequency data. The first is the Second Order Exponential (SOE) model, applicable for dichotomous classifications. It uses parameters θ_i and θ_ij, where θ_i represents the log of odds of marginal probabilities, and θ_ij measures two-factor relationships. The second method uses a multinomial distribution and an information-theoretic approach, testing hypotheses with the twice the minimum discrimination information statistic (2I). The SOE model is detailed, with parameters interpreted as main effects and interactions in factorial analysis. The multinomial approach allows for general analysis of contingency tables, aligning with variance analysis. The SOE model is particularly useful for multi-dimensional dichotomous data, while the multinomial approach is more general. The thesis also discusses computational methods for estimating parameters, including iterative techniques and the use of maximum likelihood. The program developed handles up to ten factors, with input formats for cell frequencies and binary data. The program iteratively estimates parameters, with convergence criteria and maximum iteration limits. Challenges include ensuring matrix invertibility and handling singular matrices. The SOE model provides insights into interactions and main effects, while the multinomial approach offers a broader framework for contingency analysis. The thesis emphasizes the importance of understanding model assumptions and the need for computational tools to handle complex data.The thesis presents two methods for analyzing multi-dimensional frequency data. The first is the Second Order Exponential (SOE) model, applicable for dichotomous classifications. It uses parameters θ_i and θ_ij, where θ_i represents the log of odds of marginal probabilities, and θ_ij measures two-factor relationships. The second method uses a multinomial distribution and an information-theoretic approach, testing hypotheses with the twice the minimum discrimination information statistic (2I). The SOE model is detailed, with parameters interpreted as main effects and interactions in factorial analysis. The multinomial approach allows for general analysis of contingency tables, aligning with variance analysis. The SOE model is particularly useful for multi-dimensional dichotomous data, while the multinomial approach is more general. The thesis also discusses computational methods for estimating parameters, including iterative techniques and the use of maximum likelihood. The program developed handles up to ten factors, with input formats for cell frequencies and binary data. The program iteratively estimates parameters, with convergence criteria and maximum iteration limits. Challenges include ensuring matrix invertibility and handling singular matrices. The SOE model provides insights into interactions and main effects, while the multinomial approach offers a broader framework for contingency analysis. The thesis emphasizes the importance of understanding model assumptions and the need for computational tools to handle complex data.