The DUS Inverse Lindley Distribution and Its Application to Rainfall Data

ABSTRACT In this study, we introduce a new probability model based on the Dinesh, Umesh, and Sanjay (DUS) transformation, using the inverse Lindley (IL) distribution as the baseline. The DUS–IL model introduces greater flexibility for modeling lifetime and reliability data, especially those exhibiting non‐monotonic hazard rates and heavy‐tailed characteristics. Theoretical properties including the survival and hazard rate functions, moments, entropy measures, order statistics and methods of estimation are thoroughly derived. In addition, a Monte Carlo simulation study is conducted to evaluate the performance of the estimators under various sample sizes, confirming the consistency and efficiency of the maximum likelihood estimator. Application to a real dataset shows that the DUS–IL model yields a superior goodness‐of‐fit compared to existing alternatives. These outcomes highlight the DUS‐IL distribution as a robust and versatile framework for modeling complex lifetime data, with meaningful implications for reliability engineering and environmental analysis.