A Novel Weighted Log-Kumaraswamy Distribution: Mathematical Characterization, Statistical Inference, and Reliability Applications

Primary technique: Construction of a new Weighted Log-Kumaraswamy lifetime distribution using the weighted general family of distributions. In this paper, a new three-parameter lifetime model, called the Weighted Log-Kumaraswamy Distribution (WLKD), is proposed by incorporating the log-Kumaraswamy distribution into the weighted general family of distributions. The new model provides greater flexibility for modeling skewed and heterogeneous lifetime data. Several important mathematical properties of the proposed distribution are derived, including a series representation of the probability density function, quantile function, ordinary moments, moment-generating function, incomplete moments, mean residual life, mean inactivity time, and various entropy measures. The shapes of the density, hazard rate, cumulative distribution, and survival functions are investigated to demonstrate the flexibility of the model. Parameter estimation is studied using sixteen classical estimation methods and their performances are compared through an extensive Monte Carlo simulation study based on several performance criteria. The results indicate that the Kolmogorov estimator and some spacing-based methods generally provide the most accurate estimates. Finally, the practical usefulness of the proposed distribution is illustrated using two real datasets related to COVID-19 mortality rates and aluminum alloy fatigue-life measurements. Comparative analyses show that the proposed WLKD consistently outperforms several well-known competing models according to various goodness-of-fit measures, demonstrating its effectiveness for modeling complex lifetime and reliability data.