A Systematic Comparison of Ten Odd-G Family-Based Probability Models

Generalized probability distributions play a crucial role in statistical modeling across various disciplines. However, selecting an appropriate model remains a challenge for researchers. This study provides a comprehensive comparative analysis of ten odd-related families of distributions (five single and five double parameters) to aid researchers in choosing suitable models. To ensure a robust comparison, we selected the Weibull distribution as the baseline and applied each distribution to eight datasets exhibiting diverse characteristics, including left-skewed, right-skewed, bi-modal, tri-modal, and symmetrical patterns. The results indicate that among three-parameter models, the Odd Lindley Weibull Distribution (OLWD) demonstrated superior flexibility, while the Odd Burr-III Weibull Distribution (OBIIIWD) was the most adaptable among four-parameter models. Consequently, the Odd Lindley-G (OL-G) and Odd Burr-III-G (OBIII-G) families emerged as the most effective among the examined distributions. Moreover, the Odd-G family exhibited strong modeling capabilities for moderately skewed (left or right), symmetrical, bi-modal, and tri-modal data. However, it was found to be less suitable for highly skewed data. Based on these findings, we recommend the OL-G family (single-parameter) and the OBIII-G family (two-parameter) as promising candidates for modeling real-world data with diverse distributional characteristics.