Malaysian Journal of Mathematical Sciences, September 2026, Vol. 20, No. 3
A Tweedie and Copula Analytical Approach on The Impact of Sea Level Pressure on Rainfall Patterns
Phoon, S. W., Wong, V. W., and Tan, W. L.
Corresponding Email: swphoon@utar.edu.my, wongvh@utar.edu.my
Received date: 27 November 2024
Accepted date: 12 December 2025
Abstract:
Daily rainfall in Peninsular Malaysia shows a strong statistical dependence on Sea Level Pressure (SLP), yet the two series are often analysed separately. This study, therefore, develops an integrated framework that combines marginal Tweedie and Gaussian models with a bivariate copula, allowing both the overall rainfall process and its SLP-driven dependence structure to be quantified at four stations: Batu Embun, Kluang, Malacca, and Sitiawan over 1985-2021. Zero inflation and heavy tails in rainfall are managed with a Tweedie Compound Poisson-Gamma distribution, while the approximate Gaussian shape of SLP is maintained. Pseudo observations are generated using two marginal strategies: the Empirical Cumulative Distribution Function (ECDF) mid-ranks and the fitted Inverse Cumulative Distribution Function (ICDF). Several candidate copulas are then compared using Bayesian and Akaike Information Criteria. For each station, the same two predictive models are tested on a 20% hold-out set: (1) a direct Tweedie Generalised Linear Model (Direct-TGLM) using standardised SLP, and (2) a Copula Tweedie Generalised Linear Model (Copula-TGLM) that feeds SLP simulations from the selected copula through the Tweedie link. The Direct-TGLM provides the most accurate point forecasts, but the Copula-TGLM offers a more detailed view of rainfall behaviour. Although its average errors are slightly higher, the copula-based model accurately reflects the observed proportion of dry days and retains the heavier rain tail that a standalone Tweedie fit tends to smooth out. Therefore, while a simple Tweedie mean-variance structure suffices for average prediction, integrating this model within a copula framework is vital for capturing joint extremes, providing a more realistic basis for assessing hydrological risk.
Keywords: rainfall; sea level pressure; tweedie distribution; copula analysis; generalised linear model.
