Transformation Methods for Developing New Lifetime Distributions: A Comprehensive Review

Lifetime data analysis is essential in survival analysis and reliability engineering. Traditional distributions like the exponential and Weibull often fail to capture skewness, heavy tails, or non-monotonic hazard rates. This review examines transformation-based methods that enhance baseline distributions by introducing additional shape parameters, improving flexibility for complex patterns such as bathtub-shaped and multimodal hazards. These techniques provide parsimonious yet adaptable models suited to diverse real-world phenomena. A comparative evaluation highlights each method's strengths and applications, guiding appropriate selection based on data characteristics. This study serves as a practical reference for researchers modeling lifetime data across biomedical, engineering, and other disciplines.