Modeling to medical and economic data using: The transmuted power unit inverse Lindley distribution

Modeling biomedical and economic data accurately poses considerable challenges due to the complexity of these datasets, which frequently display variability, skewness, and heavy tails. Standard probability distributions often do not adequately represent these complexities, resulting in erroneous conclusions. This study introduces the transmuted power unit inverse Lindley distribution (TPUILD) distribution as a novel extension of the power unit inverse Lindley distribution (PUILD), developed using a transmuted transformation technique to address existing challenges. The density plots of the TPUILD highlight its significant potential for practical applications. The hazard rate function may display both increasing and decreasing patterns, offering significant flexibility in the formulation of statistical models for biomedical and economic research. Several significant properties of the TPUILD, encompassing various reliability measures, moments, incomplete moments, and order statistics are computed. The parameters of the TPUILD were estimated through the maximum likelihood method of estimation, accompanied by a simulation study to evaluate the performance of these parameters. The proposed distribution was applied to two real datasets from biomedical and economic sciences to illustrate its practical utility. The goodness-of-fit was assessed through multiple measures, revealing that the TPUILD offers a markedly superior fit in comparison to the inverse Topp-Leone, power XLindley, truncated power Lomax, truncated Weibull, exponential Pareto, Kumaraswamy Kumaraswamy, exponentiated Kumaraswamy, and Marshall–Olkin Kumaraswamy models. distributions. Due to its enhanced fit relative to established models, the TPUILD is recommended for data modeling in economic and biomedical domains.