Kumaraswamy Modified Kies Power Lomax Distribution: Properties, Actuarial Measures, and Applications

We introduce the Kumaraswamy Modified Kies power Lomax distribution, a novel five-parameter probability model that combines the features of the Kumaraswamy Modified Kies-G family and the power Lomax distribution, offering improved flexibility in modelling real-world data. The proposed model demonstrates extensive adaptability through its ability to model diverse density shapes, including right-skewed, left-skewed, decreasing-increasing-decreasing, platykurtic, and leptokurtic behavior, as well as hazard patterns like the bathtub, decreasing-increasing-decreasing, inverted-bathtub, and decreasing-increasing shapes. We derive the statistical properties of the model, including the quantile function, moments, order statistics, moment-generating function, and entropy. The actuarial measures show the model's adaptability in risk evaluation. Maximum likelihood estimation technique is employed to estimate the parameters, and a simulation study shows the effectiveness of the estimates. Three real-world applications to survival and reliability data highlight the model's better performance in handling complex patterns, making it particularly valuable for reliability and survival analysis applications. The Voung's statistic and leave-one-out log-likelihood values are used to demonstrate the model's strength over the competing models.