The alpha power reduced Kies distribution: Properties, estimation techniques, and applications to insurance and dairy datasets

In distribution theory, models are often extended by adding parameter(s) to enhance flexibility. This paper introduces and studies the Alpha Power Reduced Kies distribution, a novel generalization of the reduced Kies distribution. Its flexibility stems from its ability to model various distribution shapes, including decreasing, bathtub, left-skewed, and right-skewed; alongside bathtub and J-shaped hazard rates, making it highly suitable for analyzing real data bounded within the unit interval. Some statistical properties are investigated, and the model's parameters are estimated using seven distinct methods. Monte Carlo simulations are conducted to compare the performance of these estimators across small and large sample sizes. The practical utility of the proposed distribution is validated through its application to two real datasets. Results indicate that the proposed distribution significantly outperforms several established unit distributions based on various model selection criteria.