Abstract
Modelling dependence between non-normal environmental variables is important because conventional multivariate models may not adequately represent asymmetric distributions, nonlinear associations, and complex dependence structures commonly observed in environmental data. Wind speed, in particular, exhibits substantial temporal variability, making appropriate modelling of its dependence across different times of the day important for forecasting and renewable energy planning. This study develops a flexible Bivariate Weibull-Epsilon Distribution (BWED) for modelling dependence between two non-normal random variables. The study derives the joint probability density, cumulative distribution, conditional distributions, and copula representation of the proposed model, together with a copula-based measure of dependence. Model parameters are estimated using the Exact Maximum Likelihood (EML) method, while Gibbs sampling is employed to generate observations and evaluate the finite-sample performance of the estimators. Simulation experiments are conducted for sample sizes ranging from 20 to 5,000, the results show that parameter estimates become increasingly accurate and precise as sample size increases, with bias and standard errors decreasing substantially. A comparison with two existing bivariate Weibull models showed the BWED provides a superior fit, with an AIC of 3468.56 compared with 4257.98 and 3886.72 for the competing models. The proposed model is subsequently applied to 517 paired observations of wind speed recorded at 9:00 a.m. and 3:00 p.m. on the same day at Christmas Island, Australia, covering October 2018 to March 2020. The estimated Kendall’s tau of 0.583 indicates moderate positive monotonic dependence between morning and afternoon wind speeds. The study concludes that the BWED provides a flexible, robust, and tractable framework for modelling dependence in wind-speed and other environmental data, with potential applications in renewable energy forecasting and risk management.