Comparison of Trigonometric Distribution Families Under Classical and Bayesian Approaches

This study aims to compare the performance of trigonometric families of distributions, sine-G, cosine-G, and tangent-G, using the inverse Weibull distribution as a baseline, and to guide model selection for six different data structures. Six real datasets with varying distributional characteristics, including right-skewed, left-skewed, and symmetric patterns, were used for comparison and analysis. Model performance was evaluated using both classical and Bayesian model comparison approaches. Across all six datasets, the sine-G family consistently outperformed the cosine-G and tangent-G families using inverse Weibull as a base distribution. The trigonometric families showed strong suitability for right-skewed data but demonstrated limited effectiveness for left-skewed and symmetric datasets. For the Sin-IW model, strong goodness-of-fit performance was observed across datasets with different skewness patterns. For right-skewed datasets (Datasets 1 and 3), the model produced AIC values of 437.4989 and 118.6208 with corresponding KS p-values of 0.9359 and 0.8771. For the symmetric dataset (Dataset 2), the AIC and KS p-value were 118.0071 and 0.6631, respectively. For moderately left-skewed (Dataset 4) and left-skewed data (Dataset 6), the AIC values were 128.1826 and 112.0453 with KS p-values of 0.3138 and 0.0774. For the extremely right-skewed dataset (Dataset 5), the model achieved an AIC of 68.5246 and a KS p-value of 0.9960. Bayesian model comparison further supported the superiority of the Sin-IW model. For Dataset 1, the WAIC values were 474.40 (Sin-IW), 474.60 (Cos-IW), and 493.50 (Tan-IW), while for Dataset 6, the WAIC values were 200.60 (Sin-IW), 207.90 (Cos-IW), and 209.70 (Tan-IW), confirming that Sin-IW demonstrated a good fit for classical and Bayesian inference. These results highlight the robustness of the Sin-G family among trigonometric distributions and offer practical insights for selecting appropriate models when analyzing data with diverse distributional features.