A novel one-parameter tri-modal alpha-skew logistic distribution: mathematical and reliability theory with applications to distant astronomical galaxies and biomedical data

In this paper, we presented a novel family of heavy-tailed continuous probability distributions tailored to model data exhibiting trimodal features with various kurtosis levels in asymmetric, under-dispersed datasets across various categories of risk. The proposed model enhanced the alpha-skew logistic distribution, providing significant adaptability to represent asymmetry and various tail characteristics. Key statistical properties were established, and additional characterizations were offered. Mathematical and numerical analyses indicated that the model efficiently handled asymmetric data, especially under conditions of under-dispersion. The associated hazard rate function displayed various forms, demonstrating the model's versatility in reliability and survival analysis. Parameter estimation was conducted using the maximum likelihood method, and simulation studies were employed to assess the performance of estimators in small samples. The practical applicability of the model was further demonstrated through analyses of two real datasets. Finally, comparative analyses with alternative models employing a likelihood ratio test substantiated its better performance.