Journal of Data Science and Modeling

A Mahalanobis-Distance-Based Copula Model Averaging Approach for Dependence Modelling with an Application to the Tehran Province Earthquake Catalogue

Document Type : original

Authors

Sedigheh Shams
Mahnaz Rahmani

Department of Statistics, Faculty of Mathematical Sciences, Alzahra University

https://doi.org/10.22054/jdsm.2026.94057.1098
Abstract
Copula models provide a flexible framework for modelling complex dependence structures between continuous variables. However, several competing copula families may provide similarly satisfactory fits, making inference based on a single selected model potentially unstable. To address this issue, a Mahalanobis-distance-based copula model-averaging approach is adopted to account for model uncertainty and obtain more stable estimates of conditional exceedance probabilities. Its performance is evaluated through simulation studies across a range of Kendall's $\tau$ values and illustrated using an earthquake catalogue from Tehran Province, Iran, to examine dependence between earthquake magnitude and inter-event time. The simulation results demonstrate stable estimation across different dependence structures. In the real-data application, appropriate marginal models are fitted before applying the copula framework, and the estimated conditional exceedance probabilities vary only slightly across elapsed-time thresholds. These findings suggest that elapsed time alone provides limited predictive information about the magnitude of subsequent earthquakes and highlight the value of incorporating model uncertainty into copula-based dependence modelling.

Keywords

Copula model
Mahalanobis distance
Model averaging
Dependence modelling
Earthquake catalogue
Subjects
Journal of Data Science and Modeling
Volume 3, Issue 2
June 2025
Pages 227-251

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