A Probabilistic Framework for Dependent Migration: Modeling Multiple Dependence and Model Selection
Navin Upadhyay *
Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, U.P., India.
Himanshu Pandey
Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, U.P., India.
*Author to whom correspondence should be addressed.
Abstract
Research Problem: Migration data often exhibit complex dependence structures among migrants and their associated dependents, making conventional probability models inadequate for accurately capturing migration behavior. The presence of multiple dependence patterns can affect statistical inference and lead to inappropriate model selection in demographic studies.
Methodology: To address this issue, a novel probabilistic framework is proposed by combining the Himanshu and Poisson distributions for modeling dependent migration data. The model incorporates a conditional dependence structure that reflects demographic characteristics and allows a realistic representation of dependent migrant behavior. Model parameters are estimated using the Method of Moments (MoM) and Maximum Likelihood Estimation (MLE), ensuring reliable statistical inference.
Key Results: The proposed model demonstrates greater flexibility in representing complex dependence relationships among migrants and their dependents. Application to real demographic migration data indicates that the model provides improved goodness-of-fit and more accurate parameter estimation compared with traditional approaches. The analysis further highlights the importance of selecting an appropriate probability model for obtaining reliable and meaningful statistical results.
Main Contribution: This study introduces a flexible probabilistic framework that integrates multiple dependence structures within a unified modeling approach for migration data. The proposed methodology extends the existing literature on migration modeling and provides a useful statistical tool for demographic research, migration policy analysis, and population studies. The framework offers valuable insights into migration dynamics and supports evidence-based decision-making for researchers and policymakers.
Keywords: Dependent migrant, probability distribution, moment, maximum likelihood estimation, P-value.