On multivariate triangular-valued data

This paper addresses the modeling of triangular-valued data within the inferential framework of Symbolic Data Analysis (SDA). Triangular-valued data extend conventional interval-valued data by incorporating additional information about the mode, allowing for richer internal variability modeling beyond uniform assumptions. The triangular distribution, with its bounded and unimodal properties, offers a better fit for real-world phenomena, particularly when the data exhibit asymmetry. Although much of the previous inferential work has focused on models based on midpoints and variances, following a multivariate normal-Wishart framework, these rely on internal uniformity and symmetric distributional assumptions, which often fail to capture the true underlying structure of real-world intervals. By adopting triangular distributions to model internal structures, we aim to fill this gap and extend SDA’s theoretical foundations to accommodate triangular-valued distribution models. We propose a comprehensive approach for estimating the parameters of triangular-valued data using both Bayesian Markov Chain Monte Carlo (MCMC) and frequentist methods. Our methodology leverages skew-normal and generalized Wishart distributions to capture the complexities of triangular-valued random variables. Simulation studies are conducted to evaluate the performance of the estimators, and model comparison is performed using the Bayes factor. Furthermore, we demonstrate the practical applicability of our framework through an analysis of real climate data, highlighting the versatility and precision of the proposed model.