Bounded data modeling using logit-skew-normal mixtures

Bounded data on (0, 1) have often been modelled in several real-world applications using several distributions. However, these studies lack addressing skewness, kurtosis and heavy-tailed properties in observations. This study presents a novel skew-normal type distribution defined within a bounded interval, which is derived by integrating the structures of skew-normal distributions and the logit function. With its extended skewness and bounded properties, the proposed model provides a versatile and suitable solution for modeling rates and proportions. We have developed an EM-type algorithm to accurately estimate the model parameters and its finite mixtures. To illustrate the effectiveness of our approach, we conducted experiments that included two simulation studies and an analysis of real data. The results highlight the flexibility and accuracy of our proposed model in comparison to traditional mixture models.